´

# new linear codes from 040110

## binary q=2

```q=2 k=9 n=43 d=18 optimal

(using automorphisms)

code with group 35832

generator matrix:
0000000000000000000001111111111111111110000
0001000100110111011110000000011011100110011
0010001001011011101110000000101101111001100
0100010011001101110110000001100110100110011
1000100010101110111010000001010111011001100
0000011010000010101110000111011000101110001
0000110000100001110110001010111100011010100
0000100100011000111010010011101010010110010
0000001101000100011110100011110001011101000
corresponding to the solution:
[0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,1,0,0,1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0]
mindist=18
weight enumerator=1 [0]  138 [18]  129 [20]  73 [22]  92 [24]  44 [26]  33 [28]  1 [30]
1 [32]
```
```q=2 k=9 n=51 d=22 optimal
(using automorphisms)

code with group 35832

generator matrix:
000000000000000000000111111111111111111111111110000
000000010001001101111000100010011001101111111010011
000000100010010110111001000100101010110111111101100
000001000100110011011010001001100110011011111010011
000010001000101011101100010001010101011101111101100
000100001011111010011000010010100000101000111100111
001000000111101111001000000111000010000101011011101
010000001110011101101000001100010100000011101101011
100000001101110100111000011000001001010001110011110
corresponding to the solution:
[1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0
,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0]
mindist=22
weight enumerator=1 [0]  164 [22]  85 [24]  120 [26]  32 [28]  84 [30]  9 [32]  16 [34]
1 [40]

```
```q=2 k=9 n=59 d=26 optimal
(using automorphisms)

code with group 35823

generator matrix:
00010001000100010001011111111011100110011010011001111000100
00111111001100110011001100111001101010101010101110000011000
01010011111101010101010100111010111001010100000010100000000
01100101111101011001010101010000000110101001010010101101001
01011100011011110101010101011000001010110011111001100010100
00110110000011110011110001100111101101100110000100100000000
00000000000000000000111100000111111111111111111111111111111
00110110111100000011110010010000010010011110000011000111100
11111111000000001111111111110000011111111000000111100000000
corresponding to the solution:
[1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0
,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,1,0]
mindist=26
weight enumerator=1 [0]  173 [26]  88 [28]  116 [30]  23 [32]  66 [34]  16 [36]  28 [38]
1 [42]
```
```q=2 k=9 n=62 d=28 optimal
(using automorphisms)

code with group 35823

generator matrix:
00010001000100010001011111111011100110011010011001111000100000
00111111001100110011001100111001101010101010101110000011010100
01010011111101010101010100111010111001010100000010100000010100
01100101111101011001010101010000000110101001010010101101000001
01011100011011110101010101011000001010110011111001100010111000
00110110000011110011110001100111101101100110000100100000001100
00000000000000000000111100000111111111111111111111111111101111
00110110111100000011110010010000010010011110000011000111101100
11111111000000001111111111110000011111111000000111100000000000
corresponding to the solution:
[1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0
,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0
,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,1,1,0,1,0]
mindist=28
weight enumerator=1 [0]  261 [28]  139 [32]  82 [36]  28 [40]  1 [44]

```
```q=2 k=14 n=115 d=48
(using automorphisms)

code with group 126507

generator matrix:
0000111111110000111111110000111111110000111111110001110100111111111100000011111100000000111100000000111101111101101
0001000000010111000111111111000011110011001111110010011100000000111100011100011100001111001100000111011100001101100
0111000001111001011000110111011111110111110111111100010111000011001101101100100100010111010101111001000101110000001
1000000111111111100011011011111100011100011011110000111101000001111100101100001000011011110000111010101010110100000
0011001010111011101011010011001100110011110000110110110000000011110010100111101100110000001111000110010101011100000
1101110010111101000100110000110101110101111101010010001000111110010010101100010111101111011111000111010010100110101
1000110100111101100101110100100110111111010011100111101101001101010110011000100000011111010010000111111100111110100
0000011000000011100110100101100111111101010010101011111000010001000010110101001011110101000010111001111010110010110
0000101110000111101010000101110101000010001111100000111110110110110101010001111001111011101010001111111010110100000
0101110011110001110011011010001001000110001000101010100101000110111010110001100110011110100001110111100100101100001
0110111100110110111101010000111110011101010000111010001110100101000000000000101001111111011111010011110111001111011
1101000110101011111010100010110101100111001010100000000000111000000111001000000110110111001111000001101100000000000
0011010010001101011101010100001000000101100000011000000110010110101010011111110010100011011010110110100010010101101
0000000000001111111111111111111111111111111111110000000000000000000000000000000000000000000011111111111111111100011
corresponding to the solution:
[0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=48
weight enumerator=1 [0]  1444 [48]  2976 [52]  4362 [56]  4032 [60]  2811 [64]  672 [68]
84 [72]  2 [88]

```
```q=2 k=9 n=143 d=68 optimal

(using automorphisms)

code with group 35823

generator matrix:
00010001001100010001001100011111111100010001000111011100010111011110111110001000101001100110011011100110111010011011100110001000110001000100000
00110011111100111111001111110011001100110011001111100100111001001111111010011111101010101010101001101011001110101100101010110011000110011010110
01010101010101010011010100110011001101010101010111111101011111010111001011111001110101011001100000000001010001010101000000000101000000101010110
01100000000010100101001100110101001101011001111101111110101010011000110000110011011010100110101111111110011011001000010101111010111010101010101
01011111010101011100110011001010010111110101111111001111110101010110110100110110001100101010101100111111010000110111111110011101000101000011010
00111111111100110110011001101001011011110011111100000011110000110000011110000101011001101100110000000001001001100111100000000100100000111101100
00001111111111110000000011110000111100000000111111000000001111000001111111111000011111111110000000000000000110000111111110000111101111000000000
00110000111100110110100101100110100100000011000000111100001111110000011111111101011110010011001111100001001000011000000001111100101111000001100
11110000000011111111111111111111111100001111000000000000000000111101111000000111100111111111111000000001111001111000000000000111100000000000000
corresponding to the solution:
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0,0,1,0,1,0,0,0
,0,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1
,1,0,1,0,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1
,0,0,1,0,0,0,1]
mindist=68
weight enumerator=1 [0]  296 [68]  59 [72]  108 [76]  3 [80]  44 [84]  1 [88]

```
```q=2 k=9 n=155 d=74 optimal

(using automorphisms)

code with group 79247

generator matrix:
00000000001111111111111111111111111111111111111111111111111111111111111111111111111111111100000000000000000000000000000000000000000000000000000000000000000
01111000110001101111011110001101111000110001100011011110001100011011110001100011000110000001111000110001100011000110001101111000110001100011000110001100000
10111001010010110001101110010100011011110010101111000111110100101100010000001100011000111100011011110010100011111010010100011001010110000000011000110001111
10001011110110011110100010111101111100010010100011101110011011000100100010100011000001011110111100010010100101011111100010100000000010100101000001010010111
01010110000111110111010101100010111111010010110100110000010111101011001101100101101111101100101111010010111110100101110100000011001110111011101110010111011
00011001010111101111000110010100101101000101011101110000010101100101110101010010101000010110001101000101000101001100110001001011111011101010101000110000101
11110101000001111011111101010000110100011010010010011110001100000100100100111110001010111100101100011010011101000000000001001110110011001001001011001001111
10010110110101011101100101101110111110001001010100110111100000101010010001100101000001110111110110001001001001111010010101001000001001000011000000011011101
00011110111000110100000111101111101011000001101010111010110010100111100000010100110110011000101011000001100110010011010010010010011011100000110110011000110
corresponding to the solution:
[0,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0,1
,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,1,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,1
,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,1,1,0,0,0,1,1,1,0,0]
mindist=74
weight enumerator=1 [0]  220 [74]  135 [76]  31 [80]  70 [82]  20 [84]  20 [90]  5 [92]
10 [98]
```

## ternary q=3

```q=3 k=12 n=101 d=54

(using automorphisms)

code with group 676

generator matrix:
00000000000001111111111111111111111111110111100000000000000000111111111111111111111110111001111111101
00000011111110000011111111111112222222221012200000001111111111000000000000111111222221002110011222212
00011100001221122200000011111220112222221111200011110111111112000000011122011222001120012020202001211
11101211222010101201122200122022002222220211201100111000111121000122211212101000022220000120120120000
01220200122101222022212200202101120011220211210202220011000221112101200001210012010221101120120120002
21212200212210221201100201211120111211122212211122221002002211111121211011001102202012010010120100102
20112112012200122020101110110101000022021120011112120111112022012020211020221020101210210020210122121
01122112220122102110121100221220122201002212200001012202120001221120000202110120020002211010120100112
22202100001102210101100212111120011011222100000112011012012001210111211102111120001210210100221122121
21120022000020100210102100100201000010111112010221221110001001100210001011002210011111011020202112020
01110212202012210202210221221211000112000002220220202200201220202112102022122011202120012000000222211
22220102221101120220200111011020221200202222120210112201012212120220122200002201001010012222222121211
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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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,0,0,0,0,0]
mindist=54
weight enumerator=1 [0]  3536 [54]  14040 [57]  46150 [60]  69782 [63]  136372 [66]  126040
[69]  92740 [72]  31420 [75]  8440 [78]  2500 [81]  418 [84]  2 [90]

```
```q=3 k=12 n=115 d=68

(using automorphisms)

code with group 714

generator matrix:
0000011111111111111111100000000111111111111111000001111111111111111110000000011111111111111100000111111111111111111
0001100000111112222222201111111000001111111122001110001111111112222220011111100001111111222201111000000001111122222
0110100012012220012222210111222000120000122202010010220000011120011221101111101220001112012210002011122220000201112
1120012211120011200002201001002012210112202211100101021122222220000110210022220000110121000110121212211120002210121
0202112211121211010120212121110011102001000222021021111101201210001020201101211022012100202120220111212221122101100
1112021202220200010021100200000121000010122212210122022211121002201111120012010102221011221222022002000110211212002
1222012211121112220020020200111121111121120100201210000222120222202021200100002120202000000020001112010100020011200
1102101002010110102221112121121210210202220220011011122000011200221122110000111102011022012121200221000110021100010
0110011221212021110212211022011112021112101011100110011000120112222121212020210020010000102201122110111122210000200
2122020020102212221212202111121210110220212202212120121121212011210000110122112010000212111012100102021021102112002
0020212012212000121000001202211120210020201001202100012100020020221202221102220020001001202220102002001221010102000
2102221211012022021121012112012110011012022112102110002222212210122121121220102200101202011002102002000110120000200
corresponding to the solution:
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,0,0,0,0]
mindist=63
weight enumerator=1 [0]  4600 [63]  14904 [66]  39378 [69]  78568 [72]  119922 [75]  118818
[78]  92736 [81]  42642 [84]  16422 [87]  2898 [90]  552 [93]

```
```q=3 k=12 n=126 d=69

(extension of a code using automorphisms)

generator matrix:
000000000111111111111110000000000111111111111000111111111111111111100000000011111111111110000000000111111111111100000011111101
000111111000111222222220000111111000001111122001000000011111111222200011111100001112222220000111111000000111222100011100111010
011011122012001011222220011001111011110012212112000001100001122112201101112202220020000120111001222111222112011200001201012202
102201101202000002222220011221122000011112222122122220200220112020110010220201122210022111012120111012011002101101102011100010
200220101021012020022221102021222101210020011112111110011012202100201122020120221220112201010200022202202020110200000022222202
022111011121000202011200012220012202000221102201101222200201102121201202222000222020200222002100201120221210112111211220200222
001102112002102122201200200122101202210102221212221111012100111101121120102121100010012221212100212022110111000022010022002000
002222102011122112001111002202102020210200212020100011110100211110220212111102222111121001100200120002012010111212011121201020
120200211210021120211121012112101110010102012220110021220110122110200122011200120122111121000102220111111121200222012102101202
101000102200212220201210011112221202021000020111122111111020122122000001002112002021120220202011020001102200000222100202100020
200011121011020010122011200022021212120102022120212201110121002111002221200001202201020212122020020111012220011122212020201101
221101020011120102222210010011111200220200022012000021210220210220210102122021100220212122201112221002110100202121210110220101
mindist=69
weight enumerator=1 [0]  3236 [69]  10934 [72]  28644 [75]  61820 [78]  98192 [81]  119658
[84]  101992 [87]  67914 [90]  28710 [93]  8228 [96]  1870 [99]  198 [102
]  44 [105]
This is a self-orthogonal code

```
```q=3 k=11 n=132 d=75

(extension of a code)

generator matrix:
000011111111111100001111111111110000111111111111000000011111111100000011111111110000000111111111000011111111111110011111111111111101
111100000111222201110000122222220111000011122222000011100111111200011100000000220011111000122222001100001111112220100000000011112110
012200111001122210121122200001220011112212201122011111101111222201100100011111120111122000000011011200110001121101200001111201120211
211111022022202201000012000010021022120220000202011222212012022010202222211122200101202012101101011101121221100021100111122221121021
221112122111001221111220211200121012120200222101122211200002112011122000211202200021211022020212022201110112210221112121102220011021
021220000021120102112110111212110010211120100211202001022121201210001112201202111112020120100002100202021120012000101020211210111211
111120211020020102212212012002201120020020201100102110220122022000220210122112112200000001221110202121102210101112012100122020111101
122000112212221200112000011011122110102020021212102222001200110022001012010220021020222122001100110021201221101101122111100200102211
110210100011100120200221010021201022001021121020000222010112011202200211010210022222220000111222212020020111220022222022102210210021
211120220122111002102010200002122000222201101212011221022222221101021010202211221122222201112010002201010211102220101220212010021202
021012011002002222202021121002220012202212010002201001020200000212102102020020121110002220121222221201202010010010021220110011212101
mindist=75
weight enumerator=1 [0]  3144 [75]  7936 [78]  17056 [81]  27472 [84]  38184 [87]  37568
[90]  25536 [93]  14034 [96]  4928 [99]  1152 [102]  128 [105]  8 [111
]
This is a self-orthogonal code

```
```q=3 k=12 n=135 d=75

(using automorphisms)

code with group 934

generator matrix:
000000111111111111111100000000011111111111111000000111111111111111100000011111111111111110000001111111111111111000000111111111111111111
000011001111122222222200011111100001112222222000011000001111112222200111100000111111122220000110000011111222222011111000001111112222210
011112220011211122222201100012201221220000222000100011120222220012201012200011001122200220011020002212222000112111122001220011120011222
100211121211000011122210001120210020000122222111102201100012221101211101200101020000112011100120121221222012020000202122020001200102010
022120110111100000201202200220000202112012122111012020122010010100112012001221202201022211212200212011011100121101202000000222222202122
200011210122001211202121202121021220020112010112001221111101210020111000200210111120012200111022010202101221202200202222000021111022012
102120120112112022121200200102021111221122200011202010111122200201122020111021002202220210002100201211001221020221210222220120012000200
200200112110122002210000111201110221011012101202001020210112101002110200221001202220002101010010010002102021100101211001221100221201220
111112012210222122000021022010220010202110202102021221002020002110122002110212001220222212001110110011221121202012120012202100102100222
220102220102021011000111012112121122001202111102222111120210210001122221222212120011211002211102121202001002000201122101200020010102120
120022020121200011210021021011100211011222101100010111112212001122112210211010112010210112202110200110121000110202020111022112222110011
222001220120202020100211021112000020112211121001211201112010202111111012101121012210220010010012020220212012201102120012002211211222011
corresponding to the solution:
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mindist=75
weight enumerator=1 [0]  3080 [75]  13112 [78]  30888 [81]  61028 [84]  94600 [87]  118322
[90]  102058 [93]  65824 [96]  29876 [99]  9812 [102]  2486 [105]  308
[108]  44 [111]  2 [135]

```
```q=3 k=12 n=139 d=78

(using automorphisms)

code with group 714

generator matrix:

```
```q=3 k=12 n=139 d=78

(using automorphisms)

code with group 714

generator matrix:
0000000011111111111111100000000111111111111111000000001111111111111110000000000011111111111100000000111111111111111000000000001111111111110
0011111100000011122222200111111000000011112222001111110000111122222220001111111100011122222200111111111111111222222000111111110001111112221
1100222200122211101122211000122000122201120022010112220122012200112220110001112211201201122211011122000112222000011111001111121110011120011
0211122202201200112212201012200222011200210212100011120012120222000001000110120002110111200001001212112121112012201002021222200000112221210
1222200122220100102200101112211022102021000101022210201121201000021220012012120122101100012220112012120020020210122000211000211222122200220
0000111122211112101221200011102201000021101100200022221202001211112221211102122012210002120121011101002120221112112021221012210221020021112
1202211101012201000120202101111001112220112110202021121122210011021011011222201010201121121000121212200211102220020200212222221221010012021
1202012121021201102122102102121220002021012210022201111212201122210101220022121000201000120000102111122211201000021001100202120110121210120
1210112122000112211011122210002202101201210102120102122102000201212200022021212102100200111111000201222121011122121001202112202022111002100
1122220102200211111021112121221211020120202101021010211101211110200100012211210212100020222021112010210101012122122200221222102002200101220
1111002000000201212200220202201100120222111122002000220010012021122001000210220221221110020010212111210112121121222112212211022200122121112
0021011202102202010211102100112100202002020012220221111201011021012122010220002202021112101100011001121111011221100001200200110001111021200
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,0,0,0,1]
mindist=78
weight enumerator=1 [0]  4922 [78]  15134 [81]  32614 [84]  65412 [87]  98670 [90]  116290
[93]  98118 [96]  60444 [99]  27922 [102]  9430 [105]  2070 [108]  276
[111]  138 [114]

```
```q=3 k=12 n=155 d=87

(using automorphisms)

code with group 934

generator matrix:
00000000011111111111110000000111111111111111100000011111111111111110000000111111111111111000000000111111111111100000011111111111111110000000001111111111111
00001111100000111112220011111000011111112222201111100000011222222220111111000001122222222011111111000111112222200011100000011112222220001111110000000001222
00110112200022001120120101122122200111221222200001200001100001112221011122012220201111122100001112022111220112201101200111211110011120010011120000111222011
01011000201102010001020112202201212001010002211110201121200020011221101112101221120002201001120022001011220010110220011022101121212201111201200012002112112
11211221011200020111021121201102200011000002200120101221112102222010220122010000120110102110110120212202021210220111201001210001120200202222120101020010012
00200021201100011111021110100102110212220121011221010211021022221000111201222012012220011112110220102020111111002000020021020221000221112121211102200012010
02212101102002021000200211100200101011001101000001100221022210100111021000101111000110101110002111121210101002111010102100001010111101201121022020222220100
20101201120121011121100220012221020120212222120101010020100222201202022221210002200122000101202112200222200202122002210211011000001212110120210222002200100
20210211102202111201202122010200001111121011201100011010202000210100221122022001111002011002220120222111220110200022220122022022221121010000111012000021100
12022021000112211111020212120112012010011212120111022212000022210112221102111212122120011210002101022111210220102022211020101121100001011200021102101102200
11221112200112221000010022122210101101102110101001122201211221111000202002010012001011122200022010100200000100021000120000210020202201202212102201110012102
02210020010020002001221221221212101122112221102010102121220121200001000212122010222122001010002012001221010112222000002000222100001122002112020002010112201
corresponding to the solution:
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mindist=87
weight enumerator=1 [0]  2794 [87]  9900 [90]  22682 [93]  49148 [96]  80894 [99]  104214
[102]  104082 [105]  79882 [108]  48714 [111]  20878 [114]  6182 [117
]  1870 [120]  198 [123]  2 [132]

```
```q=3 k=12 n=165 d=93

(using automorphisms)

code with group 934

generator matrix:
000000011111111111111100000000011111111111110001111111111111111111000000000111111111111100000001111111111111110001111111111111111111000000011111111111111100011111111
000000100011111111122200111111100001111222220110000011111111122222001111111000000011222201111110001111111112220000000001111111112222001111100000001222222201101111122
111111200201111112201201000222201121122012221020112201111112200022010111222000122200002200111220110000111121120110112220001111220112110222200111220000111210120012212
000012111010112220200201002122220110211210121110021100001120022202121001011002100201120110111020010001001220111001110010120011021011010002200012011000112002220010210
022200212121120221112211122001210201001100020211120001111220101111211221101110100120201211122211010020120212000020002221220001121220100120112200101122022200022222222
201201111012002112110212200000211111112000002121100221112000120122112121002012000000000120201021212222122202122011001201011201220211021200022212110101112111220101210
000122012000102220201211121210220011200010112010222200122201100112222010020111001202212202002212000221002200221221222211102011011120112201201022022021002121122010112
200201211122110022220101210202211100222012220212000002212022202012120211211221222000012001200210212110012202222022012202101022111022120100002000211211201220222012221
100022111201220111010221121121202010001212022222201201100200002202010120010120201101222001201001010220001222202100200122200111221222000000112021121220202011010112011
000110122212021221011221002002110221000212020012210000111122010102110210210021011010100122111022220021001210201200021022001111112121110012122120112200012220200202101
001111000222202120000201201201102002022210202120021020221102011112100101201201220200121002022101120012122001110120202120100221220002111211121021112012101021221121112
201021202022212010011122022000012010110222012000121222220100101200000000220210000201001020122011101011202101100022222222011021020112020122011002022020010112112021020
corresponding to the solution:
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mindist=93
weight enumerator=1 [0]  2134 [93]  8074 [96]  22622 [99]  44462 [102]  70444 [105]  95480
[108]  105666 [111]  86372 [114]  56012 [117]  27302 [120]  9196 [123
]  2970 [126]  616 [129]  46 [132]  44 [135]

```
```q=3 k=12 n=169 d=96

(extension of a code)

generator matrix:
0000000000000111111111111111111111111111000000000000000111111111111111111111111100000000000000000111111111111111111111110000000000111111111111111111111111111111011101101
0111111111111000000000001111111111222222000001111111111000000001111111222222222200000001111111111000000011111111122222220001111111000000000000011111111112222222100212101
1001111122222000111122220111122222011122000110000011112000112220011222000011222200001110011112222011222200011112200112220110011122000011122222200111222220000112122111211
2120012202222012001100222000200012201222111120112200221112001121100001222211122200111120211220112000011201200110212011221121122202122200100011222012011111222110212100220
0100002200012121121201120022002220000002011012221202000000011200202020022201012201020201000012122111201211102020210122111100100011000111000212101100011221001121022202021
1200200020100001121200020202002200210011200102121101120121121011100211201221222211120102101202100001200101220220011210222002200122222001011221021012100001222221110102220
2012110210122220221000001000010120220222202001120012002102122220210202120200000222020011121012010002201001202002220112120201102102111210101121010210212011122211112221211
0220222200201120220012102020220122120112121201120011010022111020020002000110201110112011001222110101111201020022122222212002012210100222111000122212211101011101100212220
2210201201010021001210202112202022020121222020120221221022012010100210100010022022112101110220201012001122200220001200121100201212212021121111211001220001010212112221211
0110121202202222202212001112122100011212100010202010020121102202201122202201210121100102000210210102220012220021201022200211012201112110010122201200222121000001222020012
1220022211210001220200120012110000020001002101120200112022002011100102000212112101110111212201111212112001211011122220102100220220220201120021122012202110122001001211101
1111102111001100000102100121220100012200112021200200121201022211001201020210121001110022112121022110221022121220001100010210222200121002011010202222020022202110001211101
mindist=96
weight enumerator=1 [0]  3044 [96]  10308 [99]  23780 [102]  47280 [105]  74760 [108]  95780
[111]  106580 [114]  76640 [117]  55760 [120]  26046 [123]  8362 [126
]  2520 [129]  560 [132]  20 [144]
This is a self-orthogonal code

```
```q=3 k=12 n=184 d=106

(using automorphisms)

code with group 359

generator matrix:
0000000000001111111111111111111111111111111111111111111111111000000000000000000000011111111111111111111111111111111111111100000000000000000000111111111111111111111111111111111111111111
0000001111110000000000000011111111111111111111112222222222222000000001111111111111100000000000000111111111111122222222222200000000011111111111000000000000000111111111111111222222222221
0001110000220000111111122200000000001111111111220000111222222011111110000000011222201111111112222000001111222200000000112200111111100001112222000111111122222000000111112222000011112222
0010020111010111000112201200111222220011111222110022111001122100012220111222202002201111122221222011220112011200011122022200011222201121110112022000111201112011112000221222001100110121
1121121001101001022022200112012012221201122001121111011020102212200012000012211001210111100221001222120121212002212222220201012011220112222010122012012120120000121022010002001201122110
0110111122020020002022212111201010010022200021000002101210200122200021012102220021221001211022121201011200110012202202020012101102121220120112002200200202221101112111211121002020122012
0200022101201120220010102020110220020220012002010122101021101110220010022221202110001011112101022211021121020020120121122002112122001101000212210221112220200101211011020212110011020222
1120102111112101212210221010101210122211222222121212110010102211201200010000100021020110011022211010122102220011121200112212222012002220110200110120012011010111212012221200220010011220
1100202111220200121202010212221202101022020221101012021021120020101011022012011211100202212000001112111201220100010210010020022221010011020010102001111022110211010001102222002112110212
1010000220111221000111100000120122020102011012211010222202102221020000111121011202210102022102202122010212101000021020220011221021010221201111121012102021222200122012101102021021212121
1201210010011020012222201111001000100101212211222101010200221022012111022120221201212001202202111211102201210011011020102012022012212211221121001200211000212101020021100121110120120222
2222100102002101102000222221100022110211010210202221011210002010101102100111100012002122120111010012200122221122201022122021212002010202221022122011001200100012121201201001111201021022
corresponding to the solution:
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mindist=106
weight enumerator=1 [0]  2196 [106]  2074 [107]  3660 [108]  3782 [109]  5978 [110]  7564
[111]  6466 [112]  10736 [113]  12688 [114]  15982 [115]  20496 [116]
20862 [117]  28914 [118]  25010 [119]  27084 [120]  26108 [121]  32208
[122]  34654 [123]  33916 [124]  33550 [125]  30622 [126]  31110 [127
]  21838 [128]  20740 [129]  14762 [130]  14640 [131]  10614 [132]  9394
[133]  6832 [134]  4636 [135]  4270 [136]  3538 [137]  1952 [138]  976
[139]  976 [140]  610 [141]  2 [183]

```
```q=3 k=12 n=188 d=108

(using automorphisms)

code with group 934

generator matrix:
00000011111111111111110000001111111111111111000000111110000001111111111111111000000111111111111111100000001111111111111110000000000111111111111000000000111111111111100000000011111111111111
00111100000111122222220011110000111111112222001111022220011110000111122222222001111000000011111222200111110000111122222220011111111000012222222001111111000001111111200001111100000112222221
11011101122122201122220100010022001122220222110122001120101220122011200111122111111011122201122012200111220112012200011221100111222001200011112110112222012220111222111111112200112110000112
11212201201111201202220101210112122211121122022102220221121120222001200012212120001200201100101111201012221110121202201010102111022012100111221021120112010120022011212220010001021020222021
00200202010201202200021101001202010102222002000000222222102121111100200220000010000102211201211012010011110120022022201220221112112110200002021020211010220212200012002221211201020102002002
01112102211001212020122221101212220211122021111101120201010221001121002110122101121002111200001110001220020011120021211002100022222011122022220121102112111200201002100122200012021102222211
12002121111222002212112210110002000120111100122120120210100022012111101012122200021012011221112020222002120201121102102201012011000202111220112202010111022021212210022111021022020220022100
12020212111222122012102212212202001220122010121100021221210210012222100100200201202112201200112211021201102000120120002111010012211012221021202010100202000010110001211222100121022201002222
11102020021002111020202001021012221010210010012001200200122001111010111011211002122202112112120011002121211121012011101120000200201200122101111002112200010202000010221210011220002021220002
21022001020202002222001112211201112110212011220010121210012200100001221121011212222211112010020021021201212011211122211012002200011111011201001110200210111110121201021201001222120021210212
21221221110012211221200001100101122210210201020122211101001201200011122211212020100121011011021011012122222212011221020201220120021001221020121112212210022011200212000212022111210120121101
12201120221212201221110212010200011101122002112121111111121120000111020212111110011101211111221000220101110110201001111120120212212220200110202110000020222120201211020120012122022120021111
corresponding to the solution:
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
mindist=108
weight enumerator=1 [0]  3432 [108]  10032 [111]  22132 [114]  42614 [117]  66836 [120]
89276 [123]  99308 [126]  85206 [129]  59666 [132]  32758 [135]  13508
[138]  5236 [141]  1194 [144]  198 [147]  44 [156]

```
```q=3 k=12 n=203 d=117

(extension of a code)

generator matrix:
00000000000011111111110000111111111111111111000000111111111111111100000000011111111111110000000111111111111111100000000011111111111110000001111111111111111000000000111111111111100000011111111111111111111
00000000111100001122220011000000011112222222001111000001111222222211111111100000011122220111111000000001111122200111111100000111122220011110000000112222222000011111000001111112211111100000001111112221001
00011111012200120100220101001112200110111222010111111120022001112200000122200011201111120001122011111221111212211000112201122011201120111220001122110011112011101122001120111120100112201222220001110002222
01100112010212221111020012120110222022001002001000001220201121220201122201212211221202221012212200112001112202202122000122222012100220102120020201110200121101200102120102001202201010200011120122221121001
10202020120001012202121202101110111110122112122001221222110111122201201112100111020100021120222100011010121022220102012011202101222211100120101110121211101101112201111101020211020001011101201221221212222
10120110001200212201020111002122102000200111000020012120000022012101210221121212110021110110110202121200021020001101221121012120012201122222220211012002100021222111202221010020120200201221122210112201221
02221000212120202220112122211020220220112222122122011002211022121211011201111201100220202011102200020000011111021121121221122211211021202200202021021001001210101212111221112020111102200210001122011220000
02100112121102012212101212011011211202002022112020100100102112112221101012122012000102001201021112020011002200122121001011100200020022212210110202201011201101121222021121100001211210100002011222202222002
12211212211202120110222001111112122020212122012200221202211201011211120111122111012110112121102210122012000202220012221010221120000021121210112112011021121222220222022022202011020021011001020001010102222
21122021211202101112122021111001202020020102211121221112010120220100020101200220211110212221210212211101122101101011212010220202212010110212220220102210112122202122121120201221221011111011210110201002002
10010222011210110221111020022012102201102212222202221002221112112222101102012011202221202201021010111001111022101220222112011120020211201022210102001201100120020102102110111200002011011221102201120211111
22220120200021122110120202210100212111002121012202212000100111200222210112212002102202010201022000220022102202110020200010220012212120212010020010112120201111201202001220021200000200211220100011202211111
mindist=117
weight enumerator=1 [0]  2574 [117]  8580 [120]  19998 [123]  36982 [126]  60016 [129]  77396
[132]  91942 [135]  86746 [138]  72314 [141]  42020 [144]  20438 [147
]  8888 [150]  2816 [153]  616 [156]  90 [159]  22 [165]  2 [180]
This is a self-orthogonal code

```
```q=3 k=12 n=212 d=123

(using automorphisms)

code with group 934

generator matrix:
00000000011111111111110000000000111111111111000000111111111111111100111111111000111111111111111111100000011111111111111110000000000111111111111000000000000111111111100000011111111111111110000001111111111111111110
00011111100001111112220000011111000011112222011111000111111112222201001111122111000000111122222222200111100000000111122220001111111000111222222000011111111001122222200111100000000111122221111110000001111112222101
00100022201121111221220001101222011200111122101222112000111120011211220012212002011122012200111111211000100000122122201220110001111012001000122011100011112020200011201000100012222012201110011220001121111120111220
11201202220210111121120111200022102202120002111000012001122201112221020201121221101202120011001222112001001222022011120111110120122101012011011000111101121100002212011112000100122212210010001001221200012211011101
01021100201212022111220012220001012211210212222012110120001120211100222222222011202020200202122001212120021012001100110012112222212110201202201101000220211221211221002021102010101101200110221002120120201220200220
20022002200110112010221012100100102212222121222112100101100102111112022120110011112010021201212222000202012211212202111012021212211011112020010110102210002211001222100010221102111010011200220020102211001222112122
21002201020211102121020011012000000202122000020101111010020101022011000202011011021000220110002121021121012102020201001122100202120101000220201011002222001110201111102101002022121112201012010101112100000100122000
12200002110212012112202201202212012020210211012202102110110001010022212010120121122112011110211000020020100002122122200101012101022121211201100202102211001100202001122112210020210122122110001221121210110110121202
10112000112010220111002002121211010110020112200201011210202021010100221001210112122021222200010222022110210010212101121012020212000102002001111111211212122220111220022100210100021222001021101102011211222221211220
12221000222112122101211001212002222110002020110210021121000120222222201210201200112212121011020202212100020102202111110222102011001220001210202212002101220010001122011220100002102012111221221011121021100002212202
02100122020120202200110022110000202102011012000222021111222112100202212221110111221011012211201020021112121001002001002010021011221002211221010110122101101201010212110122000010100022211212201000111002100112021110
12221221020202102210101201121211120202221120201210002122211112002201002201220120121000112120201222210200110111020220101101122221120001011211212112220122110221012002020001012010120102112202111120211211122210021110
corresponding to the solution:
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mindist=123
weight enumerator=1 [0]  2796 [123]  8382 [126]  21978 [129]  37312 [132]  55924 [135]  81840
[138]  90156 [141]  86570 [144]  67474 [147]  43472 [150]  22946 [153
]  8890 [156]  2860 [159]  748 [162]  88 [165]  2 [168]  2 [189]

```

## q=4

```q=4 k=7 n=143 d=100

(extension of a code)

generator matrix:
[[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]:[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]:[0,0]:[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]:[0,0]:[0,0]:[0,0]:
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[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]:[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]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,0]:[0,0]:
[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:
[0,0]:[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]:[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]:[1,1]]
[[1,1]:[0,0]:[0,0]:[0,0]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[0,1]:[0,1]:[1,0]:
[1,0]:[1,0]:[1,1]:[0,0]:[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:[0,1]:[1,0]:[1,0]:
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[1,1]:[1,1]:[1,1]:[1,1]:[0,0]:[0,1]:[1,0]:[1,1]:[0,0]:[0,0]:[0,0]]
[[1,0]:[0,1]:[0,1]:[1,0]:[1,0]:[1,1]:[0,0]:[1,0]:[1,0]:[1,0]:[1,1]:[0,1]:
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[1,1]:[0,0]:[0,0]:[0,1]:[0,1]:[1,1]:[0,0]:[1,1]:[1,1]:[1,1]:[0,0]:[1,1]:
[1,1]:[0,0]:[1,1]:[0,0]:[1,0]:[0,0]:[0,1]:[1,1]:[1,1]:[0,0]:[0,1]:[0,1]:
[1,1]:[1,0]:[1,1]:[0,0]:[1,0]:[1,0]:[1,1]:[1,1]:[1,1]:[0,0]:[0,1]:[1,1]:
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[0,0]:[0,0]:[0,1]:[1,0]:[0,0]:[1,1]:[0,0]:[0,0]:[0,1]:[1,1]:[1,1]:[1,1]:
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[0,0]:[1,1]:[1,1]:[1,1]:[1,1]:[1,0]:[0,1]:[1,0]:[1,1]:[0,0]:[1,0]:[0,0]:
[0,0]:[0,1]:[1,0]:[0,1]:[1,0]:[1,1]:[1,0]:[0,1]:[0,0]:[0,1]:[0,1]:[1,0]:
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mindist=100
weight enumerator=1 [0]  2865 [100]  4635 [104]  3813 [108]  3075 [112]  1755 [116]  225
[120]  15 [124]
```
```q=4 k=9 n=139 d=92

(using automorphisms)

code with group 127356

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

corresponding to the solution:
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mindist=92
weight enumerator=1 [0]  7128 [92]  4287 [94]  18495 [96]  7380 [98]  19845 [100]  15975
[102]  94500 [104]  29250 [106]  24903 [108]  10845 [110]  17820 [112
]  5220 [114]  5715 [116]  765 [118]  9 [124]  6 [138]

```
```q=4 k=9 n=144 d=96

(extension of a code)

generator matrix:
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]

mindist=96
weight enumerator=1 [0]  10827 [96]  25920 [100]  25920 [104]  132480 [108]  32427 [112]
25920 [116]  8640 [120]  9 [144]

```
```q=4 k=9 n=231 d=157

(using automorphisms)

code with group 127116

generator matrix:
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corresponding to the solution:
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,1,0,1,0,1,0,1]
mindist=157
weight enumerator=1 [0]  1002 [157]  1323 [158]  2001 [159]  2808 [160]  3240 [161]  4113
[162]  5049 [163]  6318 [164]  7959 [165]  8295 [166]  9669 [167]  11949
[168]  12420 [169]  13905 [170]  13941 [171]  14553 [172]  14931 [173
]  14967 [174]  15183 [175]  14502 [176]  14319 [177]  12933 [178]  11097
[179]  8559 [180]  8316 [181]  7020 [182]  6141 [183]  4761 [184]  3195
[185]  2781 [186]  1836 [187]  1323 [188]  540 [189]  513 [190]  432 [191
]  135 [192]  54 [193]  30 [194]  3 [195]  27 [196]

```

## q=5

```q=5 k=8 n=44 d=27

(using automorphisms)

code with group 127740

generator matrix:
11111111111111110111111111110011111100011111
02233444012233441234000111241123334401112234
11423004210222041134134133220240030111312220
20043343101422234020434114202302410134030322
31322213433123024143411223113424011211221201
11201442233204001113021200444312141241042431
24310100134022302340441242330340020203222310
22333401124224134030221403244401034233311141
corresponding to the solution:
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mindist=27
weight enumerator=1 [0]  1024 [27]  2368 [28]  5616 [29]  9200 [30]  16144 [31]  25008 [32
]  37712 [33]  51744 [34]  59376 [35]  56816 [36]  49376 [37]  36256 [38
]  22208 [39]  12048 [40]  4240 [41]  1392 [42]  64 [43]  32 [44]

```
```q=5 k=8 n=52 d=33

(using automorphisms)

code with group 127740

generator matrix:
0111111101111111111101111111011111110011111100011111
1011234410012334023401222234100011340001223311100012
4412103411411032230111233440103402201124241101201240
4304010442432343230340004222140404410403231341300322
2230404034122311024043220234302041103423133141211032
3224420132102201333343443313332231330304341031211412
1320141321242211142000310202110400011310132201232031
2201241212134120323042222002310402222212334442124104
corresponding to the solution:
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mindist=33
weight enumerator=1 [0]  1120 [33]  2656 [34]  5216 [35]  9696 [36]  15216 [37]  21312 [38
]  33264 [39]  44336 [40]  49760 [41]  53984 [42]  52752 [43]  40512 [44
]  28960 [45]  17984 [46]  8608 [47]  3456 [48]  1408 [49]  352 [50]  32
[52]

```
```q=5 k=8 n=56 d=36

(using automorphisms)

code with group 127740

generator matrix:
01111111011111111111111100111111001111110001111100001111
10012344101222340012234411000234110112331110003301110133
20412204331024240303310412012332022002240340143411342123
32120124024403243400234011314114010032033021023031320144
04243104004141421001010311300110404144102221031423140034
02431323411144332144020000220424011301242013433231101232
32334014403433012004412131244022432232122143332410313232
23013443423222423001033322031314442013431031344130144241
corresponding to the solution:
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mindist=36
weight enumerator=1 [0]  1344 [36]  2752 [37]  5120 [38]  8896 [39]  14240 [40]  20896 [41
]  32480 [42]  38240 [43]  49728 [44]  52416 [45]  50064 [46]  42112 [47
]  31584 [48]  20736 [49]  11888 [50]  5600 [51]  1776 [52]  576 [53]
160 [54]  16 [56]

```
```q=5 k=8 n=80 d=54

(using automorphisms)

code with group 128103

generator matrix:
11111111111100111111111100111111111111110011111111110111111111110001111111111111
01111234444400011112244411000011223402340101113334441000111133340011222334442233
41333410113401301130112444001234023424041120030232342024123423431123024041231324
43223203021413221410332401133400430213314222402343101342121101023431012012414323
44240122321333003200022332301024200101443021233344223312133441413231004312414220
24030143410442242442403331222320214324213123240221344302344324204402402413110023
24420231230321302430433003104211320313401141120333313242241430441430131223203344
22142301423320344202300030342141320341232303304032132033343012143012400331111122
corresponding to the solution:
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,0,0,0,0,0,0,0,0,0]
mindist=54
weight enumerator=1 [0]  1280 [54]  2944 [55]  4368 [56]  7504 [57]  12160 [58]  15680 [59
]  21968 [60]  27872 [61]  33744 [62]  39888 [63]  44224 [64]  41664 [65
]  38816 [66]  34560 [67]  25408 [68]  16848 [69]  10784 [70]  6576 [71
]  2672 [72]  1024 [73]  400 [74]  144 [75]  48 [76]  48 [79]

```

## q=8

```q=8 k=6 n=25 d=17

(using automorphisms)

code with group 127804

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

corresponding to the solution:
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]
mindist=17
weight enumerator=1 [0]  2989 [17]  6762 [18]  10927 [19]  28322 [20]  51807 [21]  62258
[22]  58065 [23]  30625 [24]  10388 [25]

```

## q=9

University of Bayreuth -