´

# new linear codes from 031110

• binary: 1 optimal + 8 new + 17 derived
• ternary: 2 new + 2 derived
• q=4: 10 new + 25 derived
• q=5: 1 new + 4 derived
• q=7: 1 new
• q=8:
• q=9: 5 new + 1 derived

## binary q=2

```q=2 k=13 n=60 d=24  optimal

(using automorphisms)

code with group 128055

generator matrix: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 to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=24
weight enumerator=1 [0]  1510 [24]  2160 [28]  3615 [32]  720 [36]  186 [40]

```
```q=2 k=16 n=74 d=28

(using automorphisms)

code with group 1185

generator matrix:
00000110001111001111100001110001111000111100111110011111000011100000111000
00011110010011110111100001110010001001111101001110100011000001101111010111
00111011110001010001100010111100011001011101010010001101001110000111101000
01100110000011010000111110010100011011100100110011101100000000001011001100
10111010010011110111111101111001101101001000100101000000010100101101101110
11011110110101010011000110100100100001111010101001110110110001001000101000
01111111111100111110101100101001110110110111010100100110111011101000110111
10100010001100101011010010011011010000000011110111110100111011000111111001
00011000011101010010001110110000100100000111100111010110001000100100111100
00000010100011101111100010011101010010101000101000000010000101100111101110
11100111000101011011101101010100101001110001111111011100111000101010011010
01011110111110010100100001110011011101100010001100000101001100001001110110
01011010111101000100010101111010001000101100001101000111111100110110010011
11001010111001001100000000011101110001010000101010110000100100001101111100
01000011000101100100010001010000110101000100010101000000010010010111010111
11001001000111010101010110100001100111111010101111101000100011110111010001
corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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mindist=28
weight enumerator=1 [0]  2240 [28]  5120 [30]  5166 [32]  4480 [34]  14080 [36]  16384 [38
]  7840 [40]  4480 [42]  2880 [44]  2304 [46]  560 [48]  1 [64]

```
```q=2 k=15 n=81 d=32

(using program of Johannes Zwanzger)
generator matrix:
000011100001110001111000111100000010011111000001100000110000011000011100000010101
001100100110110010001000011100011111100111000111101111010001111000100100011100011
110101101111010101111001100111100110101001011010110011101110100001001000100101010
111110100000010000111111011101101111010000001100010001010010001010111001111101001
011001110011010000011011101010100000000011100010011110110111111110001101111000000
000110101001100010010100001011110101011110110000010111110001001111110001011000101
100111001100110111000011110100001010011101101001100001100101110110101100101011111
100000111010110011100101111101000001011100100001011000011111101000000000101101001
111111000001000100000000010100001111010000010110100100001010110001111011001001001
010000100011000110011011100111010100000101000010111011001000010110011001000100000
100101110010100110111100001010000111111011100100001100011011001000010100000011001
010000011101111011000001111010101101000000001101111110011110001111110010111111100
010001011101100000111010110110001011111000000110000100110101011101101000001001001
010010011101011001101101010010111011000001001000101000000100010010010100101000110
010100110100111101101111010010010111110011111000110000110111100101001011100101100
mindist=32
weight enumerator=1 [0]  2199 [32]  1680 [33]  2072 [36]  3168 [37]  6118 [40]  8064 [41
]  3936 [44]  2464 [45]  1624 [48]  1008 [49]  392 [52]  42 [56]
```
```q=2 k=13 n=108 d=46

(using automorphisms)

code with group 130558

generator matrix:
111001111111111011011011011100111111111100100101101101101101101101110010010010010110010010010000000000000000
111001011111111111001001101101100101100101101100100101110110111110110110000100100000100100001110110110110010
001111101011111001111101101111101101111110101011011010000010000001001101110111010010000000000111110011000100
011011111011011001001111111111111010001011000101111100100100110110110100111111000101011100000010011011010001
100111011111001010010100010000000110111001001101100101010001000011001010101101011000101110101001000001101011
100111011100100111001111100000011100001100100000010011100101000011001010010000111001001111000010101101101101
000101110000000011000000101000001111001100001111011010100010101110100001100000000111011011100001011011101010
100111111111110110111001011110100011011111100100110010101001101100010001000101101111101000110111110110100110
001100010101110101111101100001011100011011001100101111010111011011110110011001011001111011110101000100111001
111010111101011101111000011110001011010000101100001110010000101000100110110001111101110110001001010100001010
000101000011101011101101000001111010110100011011000000000011010111000111100110111101010111011011101100000110
011000110001000101011010100100111101101001001001110011010000010110000111010110001010100101000101100101001111
111001000101100111010101001000110111001110011100110110101001110010011100001001000111011100100111010101111011
corresponding to the solution:
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
mindist=46
weight enumerator=1 [0]  924 [46]  584 [48]  1392 [50]  528 [52]  1512 [54]  456 [56]  1392
[58]  272 [60]  924 [62]  207 [64]

```
```q=2 k=14 n=112 d=48

(using automorphisms)

code with group 128605

generator matrix:
0000001111111100000011111111000000111111110000001111111100000011111111000000111111110000000000111100000011111111
0000110000111100001100001111001111001111110000110000111100001100001111001111001111110000001111001100001100001111
0111010001000100110000110011000011000011110111010111011101110101110111010111010000010000010111010100001111110000
1011000010011111010011010001010101010100110001110001101110010111110000101111100000100011110001110000110100110011
1111010000001100100000100001000010111101011011110010010010110010110001101001100011101101111111011000110101010101
1001110011100101000111011110111100111100001100111001110000111101011001011000100000010100111011100111011011101000
1000110111000111001001010011100101101001101101000100110111001010101010110111001111111111101111101001000011100111
1101100111000101100011110110101011101010010010101011011111010111010010000011000101001011010011001100000011111111
1011110100010010011000000000001000111011100001000001010010111100100010111000110000111111100000100101100110010110
0111101110000101100001100000000101000100010001011110111011101000010111000101001001001111101000010110010001100000
0001001011011101100100000000001011001010111100010101110001111111100111110001110011000001100001000001010111000101
0011010011100110011011111111001000001001001100100101001101001101001110100011100101011001010011010110111111100111
0001010100010001011111001010011110101100101111000011101000111100111010101000011111010111010101110010010000000110
1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
corresponding to the solution:
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=48
weight enumerator=1 [0]  2639 [48]  3584 [52]  3936 [56]  3584 [60]  2639 [64]  1 [112]
```
```q=2 k=13 n=140 d=62

(using automorphisms)

code with group 79662

generator matrix:
00000001111111100000001111111100000001111111100000001111111100000000011111101111000000011111111000000000111111000000000001111000001111111111
01111110000111100001110111111100111110001111100001110001111100011111111111110001000001100000011000011111000111000001111110011000110000001111
00000111111011100011111001111111001110110111100000010010001100100001100001110011000110100011101011100011001011000110000110101111010011110001
10111110011001100110111010111100010110010001100000011110010101100110100110110111011010011111101000000111010101000000011111010011000100001110
00001010111001101101010101001100011011010010111110110111101110011001011001001000000110001111100001101000111110111000100011101101101100000110
00010001001111111111001011111100001101100000100111111100101110100000011000101011000101100001100110101101000000001000000011001010011000011110
11011110001011111000000101001101101010101101001000101100000000101011100110100011101011000000000011101100010000010011001000110101010000101111
01010001100101101011011001010111110110110100011011110100100011110101100001100001111011111101100000010101000010001001001101001100001101000111
00101001000010101100110101011010000000100110110000111011101011111010101011111010101110110000111100110000011010110100110101001110111100000010
10000101010111110101100110100111001010110000001101101111001100110011100011101010110101011101110100000000010011110101001101001010001010010110
10101100111100010010110011110010110100010110110010001100111111011101000010100000000111100010111111001110100010000001111001111100101010011011
00010000100111001000001110011010011000001111010001001001110001011101110011011111001100001100100111001011111100110011010011010101101011110010
00011001110100111000101111001010010011111101011010010000011000110100111100001011101110100110101110101000011110101101000010111100100110001000
corresponding to the solution:
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0
,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=62
weight enumerator=1 [0]  1680 [62]  775 [64]  2784 [70]  1060 [72]  1680 [78]  152 [80]
60 [88]

```
```q=2 k=13 n=143 d=64

(using automorphisms)

code with group 130201

generator matrix:
00000000000000000000000000111111111111111111111111111111111100000000000000000000000000000000001111111111111111111111111100000000011111101111011
00000000000111111111111111000000000000000000011111111111111100000000000000000111111111111111110000000001111111111111111100011111111111110001101
00001111111000000001111111000000111111111111100000011111111100000000000111111000000000111111110000011110000000111111111100100001100001110011000
01110000111000011110001111001111000000011111100011100001111100000000001000001000000111011111110111100110001111000011111101100110100110110111000
00000011011000100110010011110111000000111111100001100010011100111111111000110000111000100001111011111011110001111100011110011001011001001000000
00000001100001001001110100110000000111000011100111100100011111000011111001011001011001100010110101100100010010011101111110100000011000101011000
10110110011111001010111011000000001001000000101011111100101101001100010011110010011011000000000110101000100100000100001100101011100110100011101
11011110001111001101000101011111010011100111000101111000001100010101110000001111001011100111010001100100010000101100100111110101100001100001110
10011011101000110011100000011001000011000001010000101111010110111000011100010100101100001101010111010011110000111100101011111010101011111010011
11101101100001000000011001011110100111001111010101100100001111101110001100000011001010101100000111100011100010111011010100110011100011101010110
00101011001011110111001100010000100100111101110110111011010011010000100001101010110111011001001101101000011110111101110011011101000010100000000
00011011010000101100010000010110111100100001001100101110101010111000010011100011010100010010101111010101111111000000101001011101110011011111101
10011011001000101111000001100011100011111101001110001001100111110101110101010010010000001000110010011100101111111100001000110100111100001011011
corresponding to the solution:
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
mindist=64
weight enumerator=1 [0]  2455 [64]  3844 [72]  1832 [80]  60 [88]

```
```q=2 k=17 n=182 d=74

(special construction, see  preprint)

generator matrix:
00000001111111101111000000000111111000001111111111000000011111111011110000000001111110000011111111110000000111111110000000001111110000000001111110000000111111110111100000000000111100
00011110000111110111001111111000111000000000111111011111100001111000110011111110001110000100000111110111111000011110000001110000010000111110001110011111000111110001100000111111111100
00100010011001101001010000011001011011110001000111000001100111111101110100011110000010111100011011110001111000000110001110110001110011000110110110000111011000011110100011001111001100
11001101100111110001100000100011011000010110001011100011101110001100010001100010110010011100000000011010111001111010010110010111100001001011110000101001001000000110000111000000010000
01100110100110111011100011001000011000111010010111100100000010111100101110101101110101101000011000100101011010001000101010101111111101111100011010010111000000111110111100010011000000
11111011100010110001000100101111101101000011100100000001110110010100100100001101011000100001101100101111101010011100111111011110110101111110110101100000001011101111011000100011100000
01100111100001101001011101100011010010001101111001000000000000000001011111001110111000101100100101001011111001110101110111100011100110010001101110100001110000110011001100100001100100
10111110011010101111100111010100110110100101111011000000010001101110110110111100110111000001011000001010010110111000000100101101011011101101110100111001010000101100010000110010100100
01000100111111001100101001110110111011001011101111100101111010111111100000110111000100010110110001111001100100010101101111001010001001100000110011101001011101111110101001110111011100
01000010001101100110101001110001000110110010100011101000001001000011110000011010010110001010100100110001100001011100101010100000000101101001010111011010000001101011101100011110011000
11110000111110110111100100001011001101001101001000000100100000011110110101101111101011101110000010110010110010100010000011100110100010001000001100111011100100100010111010110101110100
00011111111000011011001011100011101110011111101100111000101111101000000100100001110100000000010101010011110010101100001001111010001011010111001110110111011110100011010011111101101000
11100011010111110100110110100011100111001110100010001110101110111100011011101110110011011000101000100010010011110001000001000111011000111001101011010101100001000001110110101011101100
01101010110111111110111101110100110100000101110010000000001110010011110011001001001011011101001101000001010000111011001001001101000011010100011111101011010110000101001010000111010000
00110110111101101111001100100111000110101011010111010000101000111000111011101111001100011001100101110011110101010010111000011010110000101100100110000101101100011111011101010000110100
10100001011010011110101111101111011011001010111100101101011111001111011001000101001011101000011000101101010110101110110000011111010000010110011100111111100110011000110001001110101100
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
mindist=74
weight enumerator=1 [0]  950 [74]  1025 [76]  3600 [78]  3580 [80]  7635 [82]  8205 [84]
12295 [86]  12940 [88]  15305 [90]  15305 [92]  12940 [94]  12295 [96]
8205 [98]  7635 [100]  3580 [102]  3600 [104]  1025 [106]  950 [108]  1
[182]

```
```q=2 k=14 n=253 d=114

(using automorphisms)

code with group 129177

generator matrix:
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000000000000000000000000000
0000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111100000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111100000000000000000000000000000001111111111111110000000000000000000000
0000000000000001111111111111111111111111111111000000000000000000000000000000111111111111111100000000000000011111111111111100000000000000000000000000000011111111111111111111111111111111111111111111111100000000000000001111111111111111110000000000000000000
0000000011111110000000001111111000000011111111000000011111111000000001111111000000000111111100000001111111100000001111111100000001111111100000000111111100000001111111111111111111111111100000000111111100000000111111110000000111111111110000000111111111000
0000111100001110000011110000111000111100001111000111100001111000011110000111000001111000011100011110000111100011110000111100011110000111100001111000011100011110000111111111111111111111100001111000011100001111000011110001111000011111110001111000011111000
0011001100110010001100110011001011001100110011011001100110011001100110011001000110011001100101100110011001101100110011001101100110011001100110011001100101100110011001111111111111111111100110011001100100110011001100110110011001100111110110011001100111000
0101010101010110010101010101011101010101010101101010101010101010101010101011001010101010101110101010101010110101010101010110101010101010101010101010101110101010101010100000000000000000001010101010101101010101010101101010101010101010001010101010101010000
0011110000111100110011001100110000000011111111110011001100110010110101010011010101010010101100011110000111111010010110100110101010101010110010110011010110110100101101000000001111111100000000000000000011000011001111000001111111100000000110011110011000000
0100000110001110010001001110001011011001011111010110101110111101111101000111010111011111000101110010101000011110001101110100010101001110000101101100010010111110011011000000110000111101101111000110111100011011001010000010100110110000110010001101101000011
0010001010000110110010010101111001010011011000110110000000101001011010111011011000110101011101001111110101110100000011100111111010100111001100011000010010000010111001000011011111001100101010000110001011010010011101111000100000111100010000101100100111101
0111011111010000010111110011010111110110110001101111111001001001000101000011000001010011000100110110010100010111110011011001001110001010011111010100100101001111110101101111100011010100101010000110001011101110010010110010001101101000010000101011011001101
0011011010100000100000101011001111100011011101111110101001110010111111100101011101011110110010001000001111010011100111110110001001110000101110010010000111101111101001000101110100100010111010111111001000111001010100001010000001110011011000001011100100110
0010011100010100011101110010111000101010011100100010000011110011100100100001000100010011110011011000000010110001001110000110100000011100111010010100010010100001100011011110111001010101101111000110111110111110100011101111101010011100110011110101110110011
1111111111111110111111111111111000000000000000000000000000000111111111111111011111111111111100000000000000000000000000000000000000000000011111111111111100000000000000011111111111111111111111111111111111111111111111110000000000000001110000000000000001000
corresponding to the solution:
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1]
mindist=114
weight enumerator=1 [0]  1110 [114]  1200 [116]  1050 [118]  1110 [120]  1937 [122]  1190
[124]  1393 [126]  667 [128]  1368 [130]  1470 [132]  1305 [134]  1050
[136]  645 [138]  270 [140]  345 [142]  180 [144]  60 [146]  30 [148]
3 [166]

```

## ternary q=3

```q=3 k=8 n=154 d=96

(using automorphisms)

code with group 1325

generator matrix:
0000011111110011111111110000000011110000111111110000111111110000111111110000011111110000111111110000011111110000011111111110000111111111110000111111110000
0111101222220101111222220011111101220111001122220011011112220111001111120111100112220001011112220111100001220000101111220120001000012220120011000011111101
1001112001121010012011221100012201121122001211120100000010220112110122220001201121111111111220010012201122010111120122000000012000110000000122112201220000
1011112010021110120201020202210220010202110101110100201211111020122101201022212210120222102222211200220212200112102100122010122012210002101101120011012110
1210001110222012210110200000100120021112122100111222200122012122021111202211122110011111112020200000001022201020220201021111020000220222012100220020021012
0120122212001212012001202221102211010122200022121201011101202112002201100212022100100022000001021200201222202201010222201021102020021011021220002222012202
2010211111011120120101112102021122200120102110100202102022110012021220201121022021201012111212010122212202110112221122101201221221100212220202110110110122
2201110110121011022022111000100000001201100122001002221121121102210020101220100221100210100021202002022221122120112222001022110101220122012000011000101220
corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,1,1,1]
mindist=96
weight enumerator=1 [0]  1728 [96]  1232 [99]  2376 [105]  632 [108]  432 [114]  156 [117
]  4 [126]

```
```q=3 k=10 n=154 d=96

(using automorphisms)

code with group 132544

generator matrix:
000001111111111111111111110000000011111111111111111100000000000111111111111111000000001111111111111111110
111110000001111111112222220000011100000001111111222200011111111000000111111222000111110000000001111112221
001120011111112222220011120011101101222220000122012211100111222001122011122011111001110000011120001110011
220110001221120012220201110112220122012220012101100102212001112012211012201002012110220001111201120022220
012210112111210100121201211120010110010120120102100021101002011020200120221000002011120222211200220210202
201012121121211012012010211021112212122110210200011122210110112210212011012011201201111120100012220100112
101012220220000210120212211121220112001020210002121000001111022110010022222122020021020221201101221010112
222100012112000221201122010020210120100220211002210201211000001202021012220220102110202212212020121200100
001100101122120111100111101201112102122210020221101220020012100121222210210011021110001222112022012211112
012120210010122110210212021112002220012112200202101120011120211210100122122100200222212120110122120021000
corresponding to the solution:
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mindist=60
weight enumerator=1 [0]  2392 [60]  5902 [63]  9724 [66]  13052 [69]  13598 [72]  9542 [75
]  3796 [78]  884 [81]  156 [84]  2 [105]

```

## q=4

```q=4 k=7 n=186 d=132

(using automorphisms)

code with group 35248

generator matrix:
[[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
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[1,1]:[1,0]:[1,0]:[1,0]:[0,0]:[1,1]]
[[1,1]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,0]:[0,1]:[1,1]:[1,1]:[1,1]:[1,0]:
[1,1]:[1,1]:[1,1]:[1,0]:[1,0]:[0,0]:[1,1]:[0,0]:[1,1]:[0,0]:[1,0]:[0,1]:
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[0,0]:[0,1]:[0,0]:[1,0]:[1,1]:[0,1]:[1,1]:[1,0]:[1,1]:[1,0]:[0,1]:[0,0]:
[1,1]:[0,1]:[1,1]:[1,1]:[1,1]:[1,0]:[0,0]:[1,0]:[1,1]:[1,1]:[0,0]:[1,1]:
[0,1]:[1,1]:[1,0]:[0,1]:[1,0]:[1,1]:[0,1]:[1,0]:[0,1]:[0,1]:[1,1]:[1,1]:
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[0,1]:[1,1]:[0,0]:[1,1]:[1,0]:[0,1]:[0,1]:[1,1]:[1,0]:[1,1]:[0,1]:[0,1]:
[1,0]:[0,1]:[0,0]:[1,0]:[1,1]:[1,1]:[0,0]:[1,1]:[0,0]:[1,1]:[0,1]:[0,1]:
[0,1]:[0,0]:[1,0]:[1,0]:[0,1]:[1,1]:[1,0]:[1,0]:[1,1]:[0,0]:[0,0]:[0,1]:
[0,0]:[1,1]:[0,1]:[0,0]:[1,0]:[1,0]]

corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]
mindist=132
weight enumerator=1 [0]  3255 [132]  4200 [136]  3645 [140]  2685 [144]  1965 [148]  450
[152]  183 [156]

```
```q=4 k=7 n=197 d=140

(extension of a code using automorphisms)

generator matrix:
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[1,1]:[1,0]:[1,1]:[0,0]:[1,0]:[0,0]:[0,0]:[0,1]:[1,1]:[0,0]:[1,1]:[0,1]:
[0,1]:[0,1]:[1,1]:[1,0]:[1,1]:[0,0]:[0,0]:[1,1]:[0,0]:[1,1]:[1,1]:[0,1]:
[0,1]:[0,1]:[0,0]:[1,0]:[1,0]]

mindist=140
weight enumerator=1 [0]  3465 [140]  3450 [144]  3825 [148]  2928 [152]  1995 [156]  405
[160]  315 [164]

```
```q=4 k=8 n=128 d=88

(using automorphisms)

code with group 127962

generator matrix:
[[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
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[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]]
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corresponding to the solution:
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mindist=88
weight enumerator=1 [0]  9504 [88]  10752 [92]  25020 [96]  10752 [100]  9504 [104]  3 [128
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```
```q=4 k=8 n=134 d=92

(extension of a code)

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mindist=92
weight enumerator=1 [0]  7008 [92]  2880 [94]  8316 [96]  2304 [98]  17088 [100]  8064 [102
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```
```q=4 k=8 n=137 d=94

(extension of a code)

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mindist=94
weight enumerator=1 [0]  3840 [94]  3744 [95]  2460 [96]  2400 [97]  3840 [98]  2688 [99
]  384 [100]  1152 [101]  7680 [102]  9408 [103]  6720 [104]  3648 [105
]  3840 [106]  2688 [107]  384 [108]  1152 [109]  3840 [110]  2976 [111
]  1824 [112]  864 [113]  3 [128]

```
```q=4 k=8 n=140 d=96

(using automorphisms)

code with group 108315

generator matrix:
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[1,1]:[1,0]:[0,1]:[0,0]:[0,1]:[1,0]:[1,1]:[1,0]]

corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=96
weight enumerator=1 [0]  6195 [96]  13020 [100]  18060 [104]  16800 [108]  9360 [112]  2100
[116]

```
```q=4 k=8 n=145 d=100

(using automorphisms)

code with group 108315

generator matrix:
[[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
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[1,1]]
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[1,0]]

corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=100
weight enumerator=1 [0]  7875 [100]  11970 [104]  18270 [108]  16905 [112]  8415 [116]  2100
[120]

```
```q=4 k=8 n=171 d=118

(using automorphisms)

code with group 126573

generator matrix:
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[1,1]:[1,1]:[1,1]]

corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]
mindist=118
weight enumerator=1 [0]  3780 [118]  3990 [120]  5544 [122]  6426 [124]  8736 [126]  6939
[128]  7812 [130]  6804 [132]  6678 [134]  5166 [136]  2772 [138]  882
[140]  6 [150]

```
```q=4 k=8 n=177 d=122

(using automorphisms)

code with group 126573

generator matrix:
[[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:
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corresponding to the solution:
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]
mindist=122
weight enumerator=1 [0]  1764 [122]  4914 [124]  5544 [126]  6309 [128]  8568 [130]  7392
[132]  7812 [134]  5502 [136]  6132 [138]  6552 [140]  3276 [142]  1260
[144]  504 [146]  6 [148]

```
```q=4 k=8 n=196 d=136

(using automorphisms)

code with group 126694

generator matrix:
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corresponding to the solution:
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,0,0,0]
mindist=136
weight enumerator=1 [0]  4347 [136]  10404 [140]  14910 [144]  13797 [148]  13734 [152]
6510 [156]  1701 [160]  126 [164]  3 [168]  3 [196]

```

## q=5

```q=5 k=6 n=94 d=70

(using automorphisms)

code with group 135238

generator matrix:
0100110000000011111111111111111111111111111111111111111111111111111111111111110000000011111111
1011001111111100000000111122223333444411112222333344441111222233334444112233441111111100000000
0000001122334411114444001400140014001412341234123412341234123412341234232323231122334422223333
0000001414141412341234140023002300140034121324423121433412132442312143234114322323232312341234
0000142211443314414114142341321432412343211234123443213232232323233232411414411133224441141441
0014001441411421432143231414321423234121431324423134123232414114142323412332144114144113241324
corresponding to the solution:
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0]
mindist=70
weight enumerator=1 [0]  4128 [70]  6872 [75]  4488 [80]  128 [85]  8 [90]

```

## q=7

```q=7 k=6 n=72 d=55

(using automorphisms)

code with group 128708

generator matrix:
000001111111011111111111011111111111011111111111011111111111111111111111
111110123456101111344556100012245566101233334466100022234556000122334455
333356423556350235511046213640421615034501230424523311646034336402260536
234545264005336124316420350014364142315624614026360200645153365323033103
526346325140654365120364403624666265350213506231521612423525455640035236
111150504652130156640611164266460236461330410640241412515462103446636203
corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=55
weight enumerator=1 [0]  3024 [55]  6048 [56]  6480 [57]  4752 [58]  6480 [59]  4752 [60
]  13392 [61]  13392 [62]  32112 [63]  10800 [64]  9504 [65]  1728 [66
]  3456 [67]  864 [68]  864 [69]

```

## q=9

```q=9 k=4 n=109 d=94

(using automorphisms)

code with group 36269

generator matrix:
[[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:
[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]]
[[0,0]:[0,0]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[2,2]:[1,0]:[1,2]:[2,0]:[2,2]:
[1,0]:[1,2]:[2,0]:[2,2]:[1,0]:[1,0]:[2,1]:[2,2]:[1,1]:[0,0]:[2,1]:[2,2]:
[2,0]:[2,0]:[2,1]:[2,2]:[1,1]:[0,0]:[2,0]:[2,2]:[0,1]:[1,0]:[1,1]:[2,2]:
[1,1]:[0,0]:[0,2]:[2,2]:[1,2]:[1,2]:[2,1]:[2,1]:[1,1]:[0,0]:[1,1]:[2,1]:
[0,1]:[1,0]:[2,1]:[2,1]:[0,1]:[1,2]:[2,0]:[2,1]:[0,2]:[0,2]:[1,1]:[2,1]:
[1,1]:[0,0]:[1,1]:[2,1]:[1,1]:[0,0]:[0,2]:[2,0]:[0,1]:[0,1]:[2,0]:[2,0]:
[0,2]:[1,2]:[1,2]:[2,0]:[1,1]:[0,0]:[1,1]:[2,0]:[0,1]:[0,2]:[1,1]:[1,2]:
[0,1]:[0,2]:[1,1]:[1,2]:[1,0]:[1,0]:[1,1]:[1,2]:[1,1]:[0,0]:[1,0]:[1,2]:
[1,1]:[0,0]:[0,1]:[1,2]:[1,1]:[0,2]:[1,0]:[1,1]:[1,1]:[0,2]:[0,2]:[1,0]:
[1,0]]
[[0,0]:[1,1]:[0,0]:[0,0]:[0,2]:[2,2]:[1,0]:[2,2]:[2,0]:[0,1]:[1,2]:[2,1]:
[1,2]:[2,1]:[0,1]:[2,0]:[0,1]:[2,1]:[1,2]:[2,0]:[2,2]:[2,1]:[0,0]:[1,2]:
[0,2]:[1,0]:[0,2]:[1,0]:[2,2]:[0,2]:[0,0]:[1,0]:[2,2]:[1,0]:[2,2]:[0,2]:
[0,2]:[2,0]:[0,1]:[0,0]:[1,1]:[2,2]:[1,1]:[2,2]:[2,1]:[1,2]:[0,0]:[2,1]:
[2,0]:[0,1]:[0,1]:[2,0]:[1,0]:[0,1]:[0,2]:[2,0]:[0,2]:[1,0]:[0,2]:[1,0]:
[1,1]:[1,2]:[2,1]:[0,0]:[2,0]:[2,2]:[0,0]:[2,2]:[1,1]:[1,2]:[1,1]:[2,1]:
[2,2]:[2,0]:[2,2]:[0,1]:[1,1]:[0,1]:[2,0]:[0,0]:[0,1]:[2,1]:[1,2]:[2,0]:
[2,1]:[2,0]:[0,1]:[1,2]:[1,0]:[2,1]:[1,2]:[0,2]:[1,2]:[1,0]:[0,0]:[0,2]:
[0,1]:[0,2]:[1,0]:[0,0]:[1,1]:[0,2]:[1,0]:[0,2]:[1,0]:[1,1]:[1,2]:[1,1]:
[2,1]]
[[1,1]:[0,0]:[0,0]:[0,0]:[0,2]:[1,1]:[2,2]:[2,0]:[0,1]:[2,2]:[2,1]:[0,2]:
[2,2]:[0,1]:[0,2]:[2,1]:[0,2]:[2,2]:[0,2]:[1,2]:[1,2]:[1,2]:[2,2]:[0,0]:
[2,2]:[1,2]:[0,1]:[0,1]:[1,0]:[0,1]:[2,2]:[0,0]:[2,2]:[2,0]:[0,2]:[1,1]:
[0,1]:[2,2]:[0,0]:[1,0]:[2,1]:[1,2]:[1,2]:[2,1]:[2,1]:[1,1]:[1,2]:[0,0]:
[1,2]:[1,2]:[2,0]:[0,2]:[1,2]:[2,0]:[2,1]:[0,1]:[1,2]:[1,1]:[1,0]:[1,0]:
[2,1]:[1,2]:[0,0]:[1,1]:[2,2]:[1,0]:[0,1]:[0,0]:[2,0]:[0,1]:[0,1]:[2,0]:
[2,1]:[2,1]:[0,1]:[1,0]:[2,0]:[0,1]:[0,0]:[1,1]:[1,0]:[2,1]:[2,0]:[1,1]:
[1,1]:[2,0]:[2,1]:[1,0]:[0,2]:[2,1]:[0,2]:[1,1]:[0,2]:[0,2]:[2,1]:[0,0]:
[1,0]:[2,1]:[0,0]:[2,0]:[1,1]:[1,1]:[1,1]:[0,2]:[1,0]:[1,0]:[0,2]:[0,2]:
[1,0]]

corresponding to the solution:
[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0
,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0
,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,1,1,0,0
,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0]
mindist=94
weight enumerator=1 [0]  1232 [94]  976 [95]  1568 [96]  1024 [97]  736 [98]  368 [99]  40
[100]  32 [101]  32 [102]  32 [103]  64 [104]  168 [105]  192 [106]  64
[107]  32 [108]
```
```q=9 k=5 n=71 d=58

(using automorphisms)

code with group 80156

generator matrix:
[[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]]
[[1,1]:[0,0]:[0,2]:[0,2]:[1,2]:[1,2]:[2,0]:[2,0]:[2,0]:[2,2]:[1,1]:[0,0]:
[0,0]:[0,2]:[1,0]:[1,2]:[1,2]:[1,2]:[1,2]:[2,2]:[1,1]:[0,1]:[0,1]:[0,2]:
[1,0]:[1,2]:[1,2]:[2,2]:[2,2]:[2,2]:[1,1]:[0,0]:[0,1]:[0,1]:[1,0]:[1,2]:
[1,2]:[2,0]:[2,0]:[2,2]:[0,0]:[0,2]:[1,0]:[1,0]:[1,2]:[2,0]:[2,1]:[2,2]:
[2,2]:[2,2]:[1,1]:[0,0]:[0,2]:[0,2]:[1,2]:[1,2]:[2,0]:[2,0]:[2,0]:[2,2]:
[1,1]:[0,0]:[0,1]:[0,2]:[0,2]:[2,0]:[2,0]:[2,0]:[2,0]:[2,1]:[0,1]]
[[0,2]:[0,2]:[1,0]:[1,2]:[0,2]:[2,2]:[0,0]:[0,0]:[1,1]:[2,2]:[0,1]:[1,1]:
[1,2]:[1,0]:[0,0]:[0,0]:[0,1]:[1,1]:[1,2]:[2,1]:[0,1]:[0,0]:[1,0]:[2,0]:
[1,0]:[0,0]:[0,2]:[0,1]:[1,1]:[2,0]:[0,0]:[1,0]:[1,0]:[1,1]:[1,2]:[0,0]:
[2,1]:[1,1]:[2,1]:[1,2]:[1,2]:[2,1]:[0,2]:[1,1]:[2,1]:[2,0]:[2,1]:[0,0]:
[0,1]:[0,1]:[1,0]:[2,1]:[1,2]:[2,0]:[0,1]:[1,1]:[0,2]:[1,1]:[1,1]:[0,1]:
[1,0]:[2,2]:[0,1]:[2,1]:[2,2]:[0,1]:[1,2]:[2,1]:[2,1]:[2,0]:[0,0]]
[[2,1]:[0,1]:[2,0]:[0,0]:[1,1]:[0,1]:[1,0]:[2,2]:[1,2]:[1,1]:[1,2]:[1,1]:
[2,0]:[1,0]:[2,2]:[2,1]:[0,0]:[2,1]:[2,2]:[1,0]:[1,2]:[1,1]:[2,2]:[1,0]:
[1,0]:[2,0]:[1,2]:[0,0]:[1,1]:[2,2]:[2,1]:[1,1]:[0,1]:[2,2]:[1,0]:[1,2]:
[0,1]:[1,0]:[2,0]:[0,0]:[0,1]:[1,0]:[0,1]:[1,0]:[0,2]:[1,2]:[0,1]:[0,2]:
[0,0]:[2,0]:[0,0]:[1,0]:[2,0]:[1,2]:[2,2]:[0,2]:[0,0]:[0,1]:[1,1]:[0,1]:
[0,0]:[2,1]:[2,0]:[1,2]:[2,1]:[1,0]:[2,1]:[0,0]:[1,1]:[1,2]:[0,2]]
[[0,2]:[0,2]:[1,1]:[1,1]:[1,0]:[1,2]:[2,0]:[1,2]:[1,2]:[1,2]:[1,1]:[1,2]:
[2,2]:[1,1]:[1,0]:[0,0]:[0,2]:[1,1]:[0,1]:[0,1]:[0,1]:[2,0]:[2,1]:[2,0]:
[0,2]:[0,0]:[2,0]:[1,0]:[1,0]:[1,2]:[0,0]:[1,2]:[0,0]:[0,0]:[1,1]:[2,2]:
[1,1]:[1,1]:[1,2]:[0,1]:[2,1]:[2,0]:[0,2]:[1,0]:[0,1]:[2,2]:[0,0]:[2,2]:
[0,1]:[1,2]:[1,0]:[1,0]:[1,1]:[2,2]:[0,1]:[0,2]:[0,0]:[1,2]:[2,2]:[1,1]:
[0,2]:[2,0]:[2,1]:[1,1]:[0,1]:[1,1]:[2,0]:[1,0]:[0,2]:[0,2]:[1,1]]

corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,1]
mindist=58
weight enumerator=1 [0]  2840 [58]  3120 [59]  5040 [60]  6160 [61]  6120 [62]  8720 [63
]  8040 [64]  7240 [65]  6080 [66]  2760 [67]  2520 [68]  400 [69]  8 [71
]
```
```q=9 k=5 n=94 d=78

(using automorphisms)

code with group 80094

generator matrix:
[[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]]
[[0,1]:[0,1]:[0,2]:[1,1]:[1,2]:[1,2]:[2,2]:[2,2]:[0,0]:[0,1]:[1,0]:[1,2]:
[1,2]:[2,1]:[2,2]:[2,2]:[2,2]:[1,1]:[0,0]:[0,2]:[1,1]:[1,1]:[1,2]:[2,1]:
[2,1]:[0,1]:[0,2]:[1,0]:[1,0]:[1,1]:[2,0]:[2,1]:[2,1]:[1,1]:[0,0]:[0,2]:
[1,0]:[1,1]:[1,1]:[2,1]:[2,1]:[1,1]:[1,1]:[1,1]:[1,0]:[1,2]:[1,2]:[1,2]:
[2,1]:[1,1]:[0,0]:[0,2]:[1,0]:[1,2]:[1,2]:[2,0]:[2,1]:[1,1]:[0,0]:[0,2]:
[1,0]:[1,0]:[1,0]:[1,1]:[2,0]:[1,2]:[0,0]:[0,0]:[0,2]:[0,2]:[1,1]:[1,1]:
[1,1]:[1,2]:[0,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,2]:[1,1]:[0,0]:
[0,0]:[0,1]:[0,1]:[0,2]:[1,0]:[1,0]:[0,1]:[0,1]:[0,1]:[0,1]]
[[1,0]:[2,0]:[0,0]:[2,1]:[1,1]:[1,2]:[2,0]:[2,2]:[0,0]:[0,2]:[0,2]:[0,1]:
[0,2]:[1,1]:[0,2]:[2,1]:[1,2]:[1,0]:[1,1]:[1,0]:[0,2]:[2,0]:[1,1]:[2,0]:
[2,2]:[2,0]:[2,1]:[2,0]:[2,0]:[0,0]:[0,1]:[0,1]:[2,1]:[1,0]:[1,1]:[1,1]:
[1,2]:[1,0]:[1,1]:[0,1]:[0,2]:[0,1]:[1,2]:[2,0]:[2,0]:[1,2]:[2,0]:[2,1]:
[0,1]:[1,1]:[1,1]:[0,2]:[0,2]:[1,1]:[2,0]:[1,0]:[0,1]:[0,0]:[0,1]:[1,2]:
[0,1]:[1,0]:[2,2]:[1,1]:[1,1]:[1,2]:[1,1]:[2,1]:[1,0]:[2,1]:[1,0]:[1,0]:
[2,1]:[1,2]:[0,1]:[1,1]:[0,1]:[2,1]:[2,2]:[0,0]:[2,2]:[0,1]:[1,0]:[0,2]:
[1,1]:[0,0]:[2,1]:[0,1]:[0,0]:[0,1]:[2,1]:[1,1]:[0,0]:[0,2]]
[[2,0]:[0,1]:[2,0]:[0,2]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[0,2]:[0,0]:[2,2]:
[0,1]:[2,0]:[0,0]:[2,1]:[2,1]:[1,2]:[1,2]:[1,2]:[1,2]:[2,1]:[0,0]:[1,0]:
[1,0]:[1,2]:[2,0]:[0,1]:[1,2]:[1,2]:[2,2]:[0,2]:[1,0]:[0,2]:[2,2]:[1,0]:
[1,1]:[0,2]:[2,1]:[1,1]:[2,0]:[0,2]:[1,1]:[1,2]:[0,1]:[1,2]:[1,2]:[1,1]:
[2,2]:[1,1]:[0,0]:[0,2]:[0,2]:[0,1]:[0,1]:[2,0]:[0,2]:[2,2]:[1,1]:[0,0]:
[1,2]:[0,1]:[1,1]:[2,2]:[1,1]:[2,2]:[1,2]:[0,0]:[0,0]:[2,1]:[0,1]:[1,1]:
[2,0]:[1,1]:[1,2]:[0,1]:[0,1]:[2,2]:[0,1]:[1,2]:[0,1]:[1,2]:[0,0]:[0,1]:
[2,1]:[0,0]:[1,0]:[2,2]:[2,2]:[0,0]:[2,2]:[1,2]:[0,1]:[0,0]]
[[1,2]:[2,1]:[2,0]:[0,1]:[0,2]:[0,1]:[1,2]:[2,2]:[0,0]:[2,0]:[0,0]:[2,2]:
[1,0]:[0,2]:[1,1]:[0,2]:[0,0]:[0,1]:[0,0]:[0,0]:[2,2]:[1,2]:[1,2]:[2,1]:
[2,1]:[2,2]:[1,1]:[0,1]:[0,0]:[2,0]:[1,2]:[1,0]:[1,2]:[2,1]:[2,2]:[1,0]:
[1,0]:[2,2]:[2,1]:[0,1]:[2,2]:[2,0]:[0,1]:[0,0]:[1,1]:[2,2]:[1,1]:[0,0]:
[1,2]:[0,1]:[1,1]:[1,0]:[2,0]:[2,1]:[2,1]:[1,2]:[1,2]:[0,0]:[0,1]:[0,1]:
[0,1]:[1,0]:[0,0]:[2,1]:[1,2]:[2,1]:[0,1]:[0,1]:[1,1]:[2,1]:[1,0]:[0,0]:
[2,0]:[0,0]:[1,0]:[0,0]:[2,2]:[1,2]:[0,0]:[1,0]:[2,2]:[0,1]:[0,2]:[2,2]:
[0,1]:[2,2]:[0,1]:[2,1]:[0,1]:[0,1]:[0,0]:[2,2]:[2,0]:[0,2]]

corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0]
mindist=78
weight enumerator=1 [0]  2848 [78]  3328 [79]  4416 [80]  5864 [81]  6112 [82]  6328 [83
]  6480 [84]  6720 [85]  6336 [86]  5088 [87]  2760 [88]  1576 [89]  608
[90]  520 [91]  64 [92]

```
```q=9 k=5 n=110 d=92

(using automorphisms)

code with group 78375

generator matrix:
[[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
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[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]]
[[0,0]:[0,2]:[0,2]:[0,2]:[1,0]:[1,2]:[2,1]:[2,1]:[2,2]:[2,2]:[1,1]:[0,0]:
[0,0]:[0,0]:[0,2]:[1,0]:[1,2]:[2,0]:[2,2]:[2,2]:[1,1]:[0,0]:[0,0]:[1,0]:
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[2,1]:[2,2]:[1,1]:[1,1]:[0,2]:[1,1]:[1,1]:[1,2]:[2,0]:[2,1]:[2,2]:[2,2]:
[1,1]:[0,0]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[2,1]:[2,2]:[0,0]:[1,1]:
[1,1]:[0,2]:[1,2]:[1,2]:[1,2]:[1,2]:[1,2]:[2,2]:[0,0]:[1,1]:[0,2]:[1,0]:
[1,1]:[1,1]:[2,0]:[2,0]:[2,1]:[2,1]:[1,1]:[1,1]:[1,1]:[0,2]:[1,0]:[1,0]:
[1,0]:[1,2]:[1,2]:[2,0]:[1,1]:[0,0]:[0,1]:[0,2]:[0,2]:[0,2]:[1,0]:[1,0]:
[1,1]:[2,0]]
[[2,1]:[0,0]:[1,0]:[2,2]:[1,2]:[1,0]:[0,2]:[2,1]:[1,2]:[2,2]:[0,0]:[1,1]:
[2,1]:[2,1]:[1,1]:[2,0]:[2,1]:[0,0]:[0,2]:[2,2]:[2,1]:[0,1]:[1,0]:[1,0]:
[1,2]:[1,1]:[2,1]:[2,2]:[0,0]:[2,0]:[2,0]:[2,1]:[1,1]:[0,0]:[1,1]:[2,0]:
[0,1]:[0,1]:[0,2]:[1,1]:[0,1]:[2,0]:[0,0]:[1,0]:[1,0]:[2,1]:[2,1]:[1,1]:
[1,0]:[1,1]:[2,0]:[2,1]:[0,2]:[1,2]:[2,0]:[2,2]:[0,0]:[2,1]:[0,0]:[1,1]:
[1,2]:[1,1]:[2,0]:[2,2]:[0,1]:[0,2]:[1,2]:[2,2]:[0,0]:[0,0]:[1,1]:[1,0]:
[1,2]:[1,0]:[0,2]:[1,0]:[1,0]:[1,0]:[2,2]:[0,0]:[1,1]:[2,2]:[0,2]:[1,2]:
[0,1]:[2,2]:[0,2]:[1,1]:[1,2]:[2,0]:[0,1]:[0,2]:[2,1]:[0,2]:[1,1]:[2,0]:
[2,0]:[0,0]:[1,2]:[2,1]:[2,2]:[2,0]:[2,2]:[0,1]:[0,2]:[2,0]:[0,1]:[0,1]:
[0,2]:[2,0]]
[[1,1]:[1,0]:[2,1]:[0,2]:[1,2]:[2,2]:[1,0]:[2,2]:[0,1]:[0,0]:[2,2]:[1,0]:
[0,0]:[2,2]:[0,1]:[2,1]:[1,2]:[1,1]:[2,0]:[1,0]:[2,1]:[2,0]:[2,2]:[0,2]:
[2,0]:[1,2]:[0,1]:[0,0]:[0,0]:[0,0]:[2,1]:[1,2]:[0,0]:[1,0]:[1,1]:[2,2]:
[0,1]:[0,0]:[0,1]:[2,2]:[1,0]:[0,2]:[0,1]:[0,2]:[0,1]:[2,1]:[2,2]:[0,2]:
[2,1]:[1,1]:[2,0]:[1,1]:[2,2]:[2,0]:[1,1]:[1,0]:[1,2]:[0,1]:[0,1]:[0,0]:
[0,0]:[1,1]:[0,1]:[0,0]:[1,2]:[1,1]:[2,0]:[2,2]:[2,1]:[2,0]:[0,2]:[0,1]:
[1,2]:[1,2]:[1,1]:[0,0]:[0,1]:[2,1]:[1,2]:[0,0]:[2,0]:[0,1]:[2,0]:[0,0]:
[1,1]:[2,2]:[2,2]:[2,0]:[0,2]:[1,1]:[1,1]:[1,2]:[2,1]:[0,1]:[1,2]:[2,0]:
[2,1]:[0,1]:[2,1]:[1,2]:[2,1]:[2,2]:[0,1]:[0,0]:[2,0]:[0,0]:[0,0]:[1,1]:
[0,2]:[2,0]]
[[2,2]:[1,0]:[1,0]:[2,0]:[2,0]:[1,1]:[0,0]:[2,2]:[2,2]:[2,0]:[1,0]:[2,0]:
[2,1]:[2,1]:[1,0]:[2,2]:[0,2]:[2,2]:[1,0]:[0,1]:[2,0]:[0,1]:[0,2]:[1,0]:
[2,1]:[2,0]:[1,0]:[1,1]:[0,2]:[2,1]:[1,1]:[2,2]:[2,1]:[2,1]:[0,2]:[2,1]:
[1,1]:[1,1]:[0,2]:[0,1]:[2,2]:[1,2]:[0,2]:[0,2]:[1,1]:[1,1]:[2,0]:[1,0]:
[1,1]:[0,0]:[1,0]:[0,2]:[0,1]:[2,2]:[2,0]:[2,1]:[1,1]:[2,0]:[2,0]:[0,0]:
[1,1]:[2,2]:[0,2]:[0,0]:[0,0]:[0,1]:[1,0]:[0,2]:[1,1]:[1,2]:[1,1]:[0,0]:
[1,1]:[2,0]:[0,2]:[2,2]:[0,2]:[0,1]:[0,0]:[0,0]:[1,1]:[0,0]:[2,1]:[1,1]:
[0,1]:[0,2]:[2,2]:[2,0]:[0,2]:[0,0]:[2,0]:[0,2]:[0,2]:[0,0]:[0,0]:[0,1]:
[1,0]:[1,2]:[1,1]:[2,1]:[0,0]:[0,0]:[1,1]:[1,1]:[0,2]:[1,0]:[0,1]:[0,0]:
[0,0]:[2,2]]

corresponding to the solution:
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=92
weight enumerator=1 [0]  2560 [92]  3520 [93]  5680 [94]  4400 [95]  5400 [96]  5920 [97
]  7600 [98]  5760 [99]  5720 [100]  4000 [101]  3240 [102]  2320 [103
]  1880 [104]  880 [105]  160 [106]  8 [110]

```
```q=9 k=5 n=117 d=98

(using automorphisms)

code with group 117459

generator matrix:
[[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:
[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]]
[[0,0]:[1,1]:[1,1]:[0,1]:[0,1]:[1,0]:[1,1]:[2,1]:[1,1]:[0,1]:[0,1]:[0,2]:
[1,0]:[1,2]:[2,0]:[2,2]:[1,1]:[0,1]:[0,2]:[0,2]:[0,2]:[1,0]:[1,2]:[2,2]:
[1,1]:[0,1]:[0,1]:[1,0]:[1,1]:[1,2]:[2,0]:[2,2]:[0,0]:[0,2]:[1,0]:[2,0]:
[2,0]:[2,0]:[2,1]:[2,2]:[1,1]:[0,0]:[0,1]:[0,2]:[1,0]:[1,0]:[1,0]:[2,2]:
[0,0]:[0,1]:[1,1]:[1,2]:[1,2]:[1,2]:[2,2]:[2,2]:[1,1]:[0,0]:[0,2]:[0,2]:
[1,1]:[2,0]:[2,2]:[2,2]:[0,0]:[0,0]:[1,2]:[1,2]:[2,0]:[2,1]:[2,2]:[2,2]:
[1,1]:[0,1]:[1,0]:[1,0]:[1,0]:[1,2]:[2,1]:[2,2]:[0,0]:[0,2]:[1,0]:[1,2]:
[1,2]:[1,2]:[2,1]:[2,1]:[2,1]:[1,1]:[0,0]:[0,1]:[0,2]:[1,1]:[1,2]:[2,0]:
[2,0]:[1,1]:[0,2]:[1,0]:[1,0]:[1,0]:[1,1]:[1,2]:[2,0]:[1,2]:[1,2]:[1,1]:
[1,1]:[0,1]:[0,1]:[0,1]:[0,2]:[1,0]:[1,0]:[0,2]:[1,1]]
[[0,0]:[2,1]:[2,2]:[1,2]:[2,1]:[0,1]:[0,1]:[1,2]:[0,1]:[1,1]:[2,0]:[0,2]:
[2,0]:[1,2]:[0,0]:[2,2]:[0,1]:[0,1]:[0,0]:[0,2]:[1,0]:[1,2]:[2,0]:[2,2]:
[2,2]:[2,0]:[2,1]:[1,0]:[1,1]:[0,0]:[2,1]:[2,2]:[0,2]:[0,0]:[0,2]:[1,2]:
[2,2]:[2,2]:[1,0]:[2,2]:[2,2]:[1,1]:[0,0]:[0,1]:[1,2]:[2,0]:[2,1]:[2,2]:
[2,0]:[2,0]:[2,1]:[0,0]:[0,2]:[1,2]:[1,0]:[2,1]:[2,0]:[1,0]:[0,0]:[0,1]:
[2,2]:[2,0]:[1,1]:[2,1]:[1,1]:[2,1]:[0,0]:[2,0]:[1,0]:[0,2]:[0,2]:[1,2]:
[2,0]:[0,0]:[2,1]:[2,1]:[2,2]:[0,2]:[1,2]:[0,1]:[2,1]:[1,0]:[1,0]:[0,1]:
[0,2]:[2,2]:[2,2]:[2,2]:[0,2]:[0,0]:[1,0]:[2,0]:[1,1]:[2,1]:[1,1]:[2,0]:
[2,1]:[2,2]:[2,1]:[0,2]:[0,2]:[1,1]:[2,0]:[2,2]:[0,2]:[2,0]:[0,1]:[1,1]:
[2,0]:[0,0]:[1,2]:[2,1]:[0,2]:[0,1]:[2,0]:[1,0]:[1,1]]
[[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:
[0,0]:[0,0]:[0,0]:[0,0]:[1,0]:[0,2]:[0,1]:[1,1]:[1,1]:[0,1]:[1,1]:[1,2]:
[1,0]:[1,0]:[2,1]:[0,2]:[0,2]:[0,2]:[2,2]:[2,0]:[1,2]:[2,0]:[2,0]:[1,1]:
[0,2]:[2,0]:[1,0]:[1,0]:[2,1]:[0,2]:[2,1]:[0,1]:[0,2]:[2,1]:[1,2]:[0,2]:
[2,2]:[0,2]:[1,2]:[0,1]:[2,0]:[1,2]:[1,2]:[2,0]:[1,1]:[2,1]:[1,1]:[2,0]:
[0,1]:[2,1]:[1,1]:[1,2]:[1,1]:[2,2]:[2,1]:[2,1]:[2,0]:[2,1]:[1,1]:[2,2]:
[1,1]:[0,1]:[2,1]:[2,2]:[2,1]:[1,2]:[0,1]:[0,2]:[1,2]:[0,2]:[1,2]:[2,0]:
[2,1]:[2,2]:[0,1]:[2,0]:[0,1]:[2,2]:[0,2]:[2,0]:[2,0]:[0,1]:[0,1]:[2,2]:
[1,2]:[1,0]:[0,1]:[0,1]:[2,1]:[2,1]:[2,2]:[2,1]:[0,2]:[0,0]:[0,0]:[1,2]:
[1,2]:[0,1]:[1,1]:[1,0]:[0,2]:[1,2]:[1,0]:[2,1]:[2,0]]
[[1,1]:[0,1]:[1,1]:[2,0]:[2,2]:[1,1]:[1,2]:[1,2]:[2,2]:[1,1]:[0,2]:[1,2]:
[1,1]:[0,1]:[2,2]:[1,1]:[0,1]:[1,0]:[2,0]:[2,1]:[2,1]:[2,0]:[2,1]:[1,1]:
[2,1]:[2,1]:[0,1]:[1,1]:[1,1]:[1,1]:[2,0]:[1,2]:[0,0]:[0,0]:[0,0]:[0,0]:
[0,0]:[0,0]:[0,0]:[0,0]:[2,0]:[2,1]:[2,0]:[1,2]:[2,1]:[2,0]:[1,0]:[2,1]:
[0,1]:[1,2]:[2,0]:[2,1]:[2,2]:[2,0]:[2,0]:[2,2]:[2,0]:[0,2]:[2,0]:[2,1]:
[1,1]:[0,2]:[2,0]:[0,1]:[1,1]:[2,2]:[2,1]:[2,1]:[2,0]:[2,1]:[1,1]:[2,2]:
[0,2]:[2,1]:[1,0]:[0,1]:[1,0]:[2,0]:[2,1]:[1,2]:[2,2]:[2,0]:[2,2]:[0,1]:
[1,1]:[2,1]:[1,0]:[0,1]:[0,0]:[0,2]:[2,1]:[1,1]:[1,1]:[1,2]:[1,2]:[0,2]:
[1,0]:[0,2]:[1,0]:[1,0]:[1,1]:[1,1]:[2,1]:[1,1]:[2,0]:[0,1]:[0,0]:[2,1]:
[2,1]:[0,2]:[2,2]:[2,0]:[0,1]:[2,1]:[2,0]:[1,0]:[1,0]]

corresponding to the solution:
[1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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]
mindist=98
weight enumerator=1 [0]  2432 [98]  3696 [99]  4208 [100]  4192 [101]  6304 [102]  6656 [103
]  6304 [104]  5344 [105]  5472 [106]  3696 [107]  5152 [108]  1984 [109
]  2176 [110]  832 [111]  400 [112]  136 [113]  64 [114]

```

University of Bayreuth -