´

new linear codes from 150210

• binary: 1 optimal + 4 new + 7 derived
• ternary: 8 new + 14 derived
• q=4: 5 new + 9 derived
• q=5: 2 new + 1 derived
• q=7: 1 new
• q=8: 1 new + 1 derived
• q=9:

binary q=2

```q=2 k=16 n=83 d=32

(extension of a code)

generator matrix:
00000000000000000000000000000000111111111111111111111111111111110000110001111110000
00000000000000000011111111111111000000000000001111111111111111110001010000001111011
00000000000111111100000111111111000001111111110000000111111111110000110000110000000
00000111111000001100001000000111001110000001110000011000000011110011110010011111011
01111000011011110000010000111000000110011110110000100000011100110100011100100111000
10111000001001110001101001001111010110100011110011001000001111011001000101110000101
01111111111000010000001110001001010011000001011111001001101100110111100000010010101
00001011110000100110111111010010111001101111000101101011110101100001100000111111011
01010101101000011101110110010001010111101110101001011101101111001101101111110011110
00001010000100111001100010001110011101011110110001110011111100100101111101010110011
00001110101100101101000100001110001000010110100110001001101011100110001101100101110
00110000011010010110100010100100010110101000000000100110101000111111110011111001000
01001011010000111100101001101011110111111000011010100010001100011101100101100001101
11000101101011110110011001101100011110110010110110010100111110000001011101000111011
00001010010101110000101101111110101100111011011001000011100101001111110000011011110
11011111010101111111111000100011011001010010101111111100000101110110111000100011011
mindist=32
weight enumerator=1 [0]  3054 [32]  3072 [34]  5184 [36]  3264 [38]  16032 [40]  11520 [42
]  11008 [44]  4224 [46]  4464 [48]  2304 [50]  1216 [52]  192 [54]  1
[64]
```
```q=2 k=16 n=91 d=34

(extension of a code)

generator matrix:

0000000111111111110000001111111111110000011111111111110000000111111111110000000011111111111
0001111000001111110011110000111111110001100000001111110011111000000111110001111100000001110
0011111111110111110100010111000001110110100011110011110100111001111001110110111100011110111
1100001001111000111001101001000111111011111100010001111011011000111000010010011101100110111
0100110000111000010100001011000110110001000001111110110011000110011010110100101101101010001
0100111110111011110000110111001111010001100100110101110001101011011110001110100100010000111
1100000011000111110111100111001111010011101000100111010000001110001100001010101110111100001
1001000101010011011001001010010111000101000101001000100101001101101011010110111111101011110
1100001101000001111010110101101001010010110001100101101000111100100110000010010111011011010
0100011110001100101100110001101001110110100000100001100011010001100010001001111111001100110
1100010001000111111100011010101011011011101101001000100110000000011011100100111110000000001
0000101111011101000101100011110000101001010101111101100011001011011001011000110111010111111
0011110110100111100100000011101111000010101010111011110011110111111001000001010100100000001
1100010001100001011001010001000010100011111011100011010101101110110100110001101010111001111
1010001010010100000111110000110000100100001010010011001011011011001010010011101111110111000
0000101110001010111011101111010000100101101110111010110100111100101000010111101110011111000
mindist=34
weight enumerator=1 [0]  1071 [34]  1215 [36]  4266 [38]  3069 [40]  12387 [42]  5265 [44
]  16118 [46]  4455 [48]  11349 [50]  2025 [52]  3214 [54]  315 [56]  729
[58]  39 [60]  18 [62]
```
```q=2 k=16 n=94 d=36

(extension of a code)

generator matrix:

0000000111111111110000001111111111110000011111111111110000000111111111110000000011111111111011
0001111000001111110011110000111111110001100000001111110011111000000111110001111100000001110000
0011111111110111110100010111000001110110100011110011110100111001111001110110111100011110111011
1100001001111000111001101001000111111011111100010001111011011000111000010010011101100110111101
0100110000111000010100001011000110110001000001111110110011000110011010110100101101101010001101
0100111110111011110000110111001111010001100100110101110001101011011110001110100100010000111011
1100000011000111110111100111001111010011101000100111010000001110001100001010101110111100001101
1001000101010011011001001010010111000101000101001000100101001101101011010110111111101011110110
1100001101000001111010110101101001010010110001100101101000111100100110000010010111011011010000
0100011110001100101100110001101001110110100000100001100011010001100010001001111111001100110110
1100010001000111111100011010101011011011101101001000100110000000011011100100111110000000001101
0000101111011101000101100011110000101001010101111101100011001011011001011000110111010111111011
0011110110100111100100000011101111000010101010111011110011110111111001000001010100100000001011
1100010001100001011001010001000010100011111011100011010101101110110100110001101010111001111011
1010001010010100000111110000110000100100001010010011001011011011001010010011101111110111000110
0000101110001010111011101111010000100101101110111010110100111100101000010111101110011111000110
mindist=36
weight enumerator=1 [0]  2286 [36]  7335 [40]  17652 [44]  20573 [48]  13374 [52]  3529 [56
]  768 [60]  18 [64]
This is a self-orthogonal code

```
```q=2 k=12 n=106 d=46

(extension of a code)

generator matrix:
0000111111110000001111110000111111110000001111110000111111110000001111110000111111110000001111110110111100
0011000011110001110001110011000011110111110001110011001111110111110001111111000011110000010000010110110000
0111001101110110010010111101001101111001110011110011010001110000111111111111001100110001110001111001001010
0000110100010011100100110111110100110000110000110101100110010001110010000001011100000011110010100010010110
0100010000111100111111110000010000011000110011011011100000110110001111110110000100010100000110100000001100
0011011011111110011011010001100010010011110101000001011111000110011100010011110001101110000001001010101011
0011111000100110101011110111110001001101011111000101110011001111010100111101110111111000100010100111000111
0011000001100010010010011011110001001111100101010011011101000000001000101000001110111100100100110011101101
0001011100001011100100011110110000011010101111101100101000001110000111001111010110101101100000001111110110
0100010000001110011001000011001100110110111010001010011010010010111101000001111110110100000000101110000001
0101101011000111000001000011000001101001101000000101100111110110010101011010100000101000000111110100100110
1101101101010001000100000000111111001011001000001001111001111000100111010100110000010101111011011111110110
mindist=46
weight enumerator=1 [0]  797 [46]  516 [48]  1800 [54]  432 [56]  474 [62]  75 [64]  1 [78
]

```
```q=2 k=12 n=109 d=48 optimal

(using automorphisms)

code with group 128975

generator matrix:
0011110011110011110011110011110011110000110000110011110011110011110011110000110110110000110011111100111111000
0101110100010000111100110101110101110111010111011100111100110101110100010001010110110111011100110000000000000
0110111000110100110100110110011110111011110011111111110011110100111100110011111001001001101100001101000100110
0010011111010001110100111101110110010001000111100011000000000010000011000111100010011110000101000001001011110
0000110001011111110100010100010000001001110000111101011111111110011001001000100000000011110000001100011011000
0101110010011110010101000111100101000111010001010100101111000001100101111100001010101001110111011010000110111
0100101111000110111111001110100100101010111101011001111101010010100111100010100111001010111111110110001001111
0100100111000000011001010111001100101111010000000011110010010101100100011010110011101001101000101010010001001
0110001111011001010011101000001000001101111000101101101101101011000001101010001111111110001101100011000011110
0000000100111110001110000010110110010101100011000011110111101101001001001000101110001001010111100100000010001
0101000100000100000010001101110100111011000001010100101101100010111010110000110100101100011010000010011111110
1110010011100001000010000110010011101110001010111000010001101011111010111011011111110100000011000001101111110
corresponding to the solution:
[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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0
,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
,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
,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0
,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1
,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
,0,0,0,0,0,0,0,0,2,0,1]
mindist=48
weight enumerator=1 [0]  1313 [48]  2232 [56]  549 [64]  1 [80]

```

ternary q=3

```q=3 k=10 n=47 d=24

(extension of a code)

generator matrix:
00011111000111111000111110011111100111111011111
00100222111000122111011220100111200001112110101
01202022002011222001002121012112111020221211012
02222202120101122021201012102001112002120210121
11220101202120100222001102202001011121010011202
11100120201020020220102012021222020000010111220
12211111200201110221000110110011222211100000002
01000201200100210001121120000012102012101112121
20022001210220221010200202200011201122020220200
22110010121100102000000000202101220010111002201
mindist=24
weight enumerator=1 [0]  2344 [24]  8406 [27]  19180 [30]  20072 [33]  7928 [36]  1052 [39
]  66 [42]
This is a self-orthogonal code
```
```q=3 k=11 n=93 d=53

(extension of a code)

generator matrix:
000000000001111111111111111111111111111100000000001111111111111111111111111111111000001110000
000001111110000000000000011111122222222200111111110000000001111111122222222222222000010120000
001110001120011122222222201122200011122201001111120111112220011112200000011111220011102220000
110000120220100000011112202200112200102210220112200112221120211222200112200122121101202221100
120122010100000201211120010122012201100202120001212020120012112000201020102101110112020210011
110200100122202210102221221001100212112100021220011111100022122111222021002211201120102220120
221001121201010122010101222221120001112201120221110110101110012021121112222112200011101110000
010210121212111120010101112021110021000212212121102101002221012220010001000012222221002221002
021100121202200021110000110201212101021211110120212101020012020021011212202211110120112010011
100111010122122012000202200011212200201220222120110210001222111011212100200201211202101112121
210002021202101221012220202121011221010100122021011220211001011202012122011202222000020211010
mindist=53
weight enumerator=1 [0]  5814 [53]  7872 [54]  3600 [55]  12150 [56]  9234 [57]  5346 [58
]  6804 [59]  3888 [60]  3888 [61]  28782 [62]  21762 [63]  15174 [64]
18468 [65]  12636 [66]  7776 [67]  3402 [68]  1944 [69]  1944 [70]  3240
[71]  1620 [72]  1620 [73]  72 [80]  92 [81]  18 [82]

```
```q=3 k=11 n=122 d=69

(using automorphisms)

code with group 62

generator matrix:
00000011111111111111000000111111111111110000000111111111111100000000011111111111110000011111111111111100000000111111111111
00111100011111222222001111000011222222220011111001122222222200001111100111222222120011100001111112222200011111000001111222
00112202200022011122010222022211122222220100112120200000111200110111211012001122121100211121111120011200000111000121122012
00001110000201100101022112100112000011121112022001201222001201011111101100120101200001212200012201201011112012002021222110
01112201212122201000121111001120112211221020222212011012012212222011112001010101221202200211211110210100120212122121222110
02011202121200211211120122200111102201222010100121000001220202212100212110211201020210012112211112112212011022202011200212
00121122111002120000200020121100020100220121121012222001021121111201102012012121100012101120200211112002100000122221202002
02021010110001100002211000021110001011000101022011210222100011111122212001010000200011112100001021211100000010100112111221
00002001210202201120212120200012010211010110220202021002102112200221210220011100112200212022000111000202220221202100210121
01112020222212202002120002011220012100010211212102100111101100200000011010120101221012200211111110210221002100210002010021
10101120111201100120220211022121000012010110000010210200121201000001000022212222210021220020102110210001010110010202100102
corresponding to the solution:
[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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,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
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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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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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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mindist=69
weight enumerator=1 [0]  3280 [69]  9634 [72]  18680 [75]  30840 [78]  41292 [81]  35720
[84]  23028 [87]  11140 [90]  3000 [93]  470 [96]  60 [99]  2 [120]

```
```q=3 k=12 n=159 d=90

(extension of a code)

generator matrix:
000000111111111111111100000000011111111111111000000011111111111111100000001111111111111110000000001111111111111000000000011111111111100000000011111111111111111
011111000000001112222200000111100001111222222001111100000001111222200000110111111122222220000111110011111122222000011111100000112222201111111100011111222221002
100112001112220120222200011011200120022012222110112200001120112011200111011001122200000120111001121200011100011011100011211122020011110011222201201112001112222
202002220010110000001211101202201001201212222001020200120220020002101122220121201200112200011021212200012200202111201212000000110101222202012210121220120001002
212010002201122211022200001212101222012121122121210202201002111010112012020100000122011010101002100201211202012111100121200200110112111221211100001122200122222
100011120020111121221200110121112021201001110120201202112121212212110000002200021101011010110222020121022001100002121101101101011111101220221220202000020121220
111000120222220000010102020100021222120000210121212200222110121202221201221201120211212200020010021100111212002100022021000111011202021210202020020122210120000
222121200112222121110222002020012202002202211121200110002221221022121122011212022002022020211222120221111120222101221110111022102102022121102021000021011222001
120222121122210102121101020022201122200101102210002010022021122211120102012121110012010121100222210222101112200010010102000001200220200122220200202102001122222
202000200002120110010110222122010002211011221110021201200010202121000202021210120121020021122120122010211212221110122211110111201222222120121011010022002212001
212012122110121012222202210002210210002222011112201222221122122000212102201110222101112120112121121011221201122011000202201101210210000120002111212111202111111
201010110010120211200102020200011011010212211111111212220102000110000010221111202100000120202100010012220211101120111011001022001212100111220000102020011001111
mindist=90
weight enumerator=1 [0]  4268 [90]  11926 [93]  28622 [96]  49126 [99]  82830 [102]  102476
[105]  101904 [108]  78606 [111]  43562 [114]  19800 [117]  6116 [120
]  1848 [123]  352 [126]  4 [135]
This is a self-orthogonal code

```
```q=3 k=12 n=164 d=93

(extension of a code)

generator matrix:
00000000111111111111111000000000001111111111110000000011111111111111100000111111111111111111000001111111111111111110000000011111111111111100000111111111111111111000
00111111000000011112222000111111110001112222220111111100111111112222200011000000111111111222011110000011111111222220001111100011122222222211111000001111111122222111
11000012111112200222222111000111121120020111120001122211000112221122201101011122011112222002011220011200011222000120110122201111200011122200122001220011111200222111
00011201000222202020012002012001220000200000220010101102001020000200200111200101201221112002102121212201201012012120122100121211101112201211212022121200001102001000
12112101012000201100122221000122221200000111121002121120220220010012100100211021001122220121022100210121000012111111201212121212020121202002022202022200121101011000
00010122020021220102222011110221200220212012120002220021122102211112210211101222202120221001001202010100111021020002102202110112212020000011101012221022100211121222
01122002011021010120012010110201001202100200012020122200010121112122112001011201112102000120012122111200212111001200111101021111002110002022000010220200121001102111
21101112002002021012101202202111211022112202202202200222211220221012101101012111201010012011002122120100222221112211211222022002000020010010110211210201022010210000
02222020112001121112122020211211020022101101012101101110112020122221102122120011202212201112200222221002100212100111220111022020201102102000101010001012111201010000
11200010002202110211111012112222211212121121101002121010210121212002022002002020111211011110011102022201200011112012122110222002200122222202221002002202122100121000
20000120111000021111222102112000101002000202021211221020001100110001202012011212210012111101011111022220202202111102202211221101101111112110101211212110102020002222
22101002221110211110122000222001021000220022212000212210211122111212010020212012102011011120201210022122202010021102112100002112021200210112222221221022221210221000
mindist=93
weight enumerator=1 [0]  3864 [93]  12788 [96]  24242 [99]  49864 [102]  77740 [105]  98808
[108]  102718 [111]  77970 [114]  49588 [117]  23506 [120]  7314 [123
]  2438 [126]  552 [129]  46 [132]  2 [141]
This is a self-orthogonal code

```
```q=3 k=12 n=178 d=102

(extension of a code)

generator matrix:
0000001111111111111111100001111111111111111110000001111111111111111000000000000111111111100000000001111111111110000001111111111111111000000000111111111111100000001111111111111110
0011110000000111112222211110001111111112222220111110000011111222222000011111111000112222200000001110000011111220001110000001112222222000111111000000111222200111110000000000122221
0101220001112011221122201110010001111120111221001110012200122112222000111111122001000011201111110220112200022020111120011121110001122011111112001112012001211001120000011222000220
1221020220221122222212201121211120011102012022020020221212212110012111000022201001020202200112222120020000102220120111201210120121201000001121000120101020101120220011201022002011
1100022022120000220112210200111211100110012112020101200201220022201002202200200222010100011001220201212222012001010011022000122212002112010222122010010111122112020102211012101000
1100211220021102122120022122112110122002020010020202101110212011221110110002101010220220201012121020211212202200200212220102020111121110212022122011220221220111102012220002111222
2010211110222120010110020110220020012000022111221212122202111012100220220100112221210220000202212110012212201012121202021110100022021212122120202201012111221100010100000002222000
1211002001020002101212111001002021121102110000102110110002200102112120100022020121102222220221201222022000012000001021221102201012001002002010200102101200102122102111020020112112
2011020012212000200121222202002000111120001012200122011102200211121010112011010212002002220212121012110001002111201102001011022022100222001010001012021201112221112220022020111120
2201220202100121110222110010020001000011212200012010222100122112000110000221000000111121222111022122121221110200101101010002111220110121021202211221001012022112012010110101112012
2102210110101022122120110022012222010121210020022222022101200022020020110201112221122020100012021022000001001022222201200001121101222221201012020121012120121000110020122202112120
2110011212001012011121111002210220020011100100201102120111002022200221211100022201120210110122100220221102110201020110202110202110010202012010202210200201120000211022202221202210
mindist=102
weight enumerator=1 [0]  4048 [102]  10824 [105]  26092 [108]  45544 [111]  75196 [114]
94160 [117]  98582 [120]  85558 [123]  51590 [126]  25476 [129]  10450
[132]  2838 [135]  946 [138]  132 [141]  4 [156]
This is a self-orthogonal code

```
```q=3 k=12 n=193 d=111

(extension of a code)

generator matrix:
0000011111100000011111111111111110001111111111111111111000000000111111111111100000011111111111111111000000000111111111111100000000011111111111110000000000111111111111000000111111111111111111011
0011101222200011100000011111122220110001111111122222222000111111000111111222200111100001111122222222000111111011111122222200011111100000011122220001111111000111222222011111000001111112222210101
1112210012211101200001211122201220220020001112200011222111011222012000122022211011201220222200012222011111122100002201222200101122201122202201221111122222022112000112101122111220111120122222022
1210100112201111000220001222220021020000120000200200122111002011111012100122211001012222002200200222001012201101220211012201202201110201201200020120100112002111001021100102001021000211200010101
0000022222201101100221212202211020021200100122002212202112222211201102001002200002020011120022000122001222222222111222220112220110212101111102001021000010000122012211110220020011002101101122022
1200122210201221222120020000112112212012000201221201211021112022002220222200112100021122001202020010122100110202001021020100201202100111001201202222111122101220220122000222200011022201120212221
1002201011022022111021020202101020101102120012110000120010021012220122110121022112112121102122120000022210200202020010212021211020012100222020212122002220022000212000221102111101222000022000000
1111200111021021012121122210122112221102020102212221122210000100100122210000121220020200002220222011002010112012221021120112100120221012221120022021202020112102102122111122221202110122120120202
0220002110202010122010111122122201000020102000021002112212122101112112211001120112020200212200011102021002100102021022101200211021022002021202102100000202100122201210122020001100202122012022022
2111001201222110100100221221000200100101010221120012010210220210201221200221120011202011100101211001012001212101100220111212222001210111121011000022011121122101022022002101101120000202002020202
0212011010021120200002210221222120011210122120201212110102122222110211000101222201120010111202022111122011011111211110122221111010110202000002121022221002200221022220221210221012022010011111011
1121112002111112021002210011110220221200012010200110122020210100122200202221021002000010121020122221000120102102000111111121022001221121022120200011200212112102100211211212022212100211111211011
mindist=111
weight enumerator=1 [0]  3498 [111]  10340 [114]  21252 [117]  39952 [120]  63316 [123]
86946 [126]  95392 [129]  86394 [132]  62326 [135]  37510 [138]  16302
[141]  6380 [144]  1434 [147]  352 [150]  44 [153]  2 [159]
This is a self-orthogonal code

```
```q=3 k=8 n=199 d=126

(computed by a program of Johannes Zwanzger)

generator matrix:
0001111111111111000111111111111111000000111111111100000001111111110000000111111111011111111111111100000011111111110000111111111111000000111111111100011111111111110000001111111111000111111111111111111
1110001111122222011001111111222212000111000000112200011110001112220000111001111122000000011122222201111100111122220011000011112222001111000011122211100001111112220000110000012222011000001111111200000
0111220011200112101120011122001202011001000012011201100221111221120111222120122202101111201200112211222222002211121102111201220122011122011200101101201120122221111111220112210111022122221222222011111
2000010201012012102200201112110202102010001200011211200220110010211022012211000011120002220101010121012211020011101110112000121100011202101002211222020122000120120112002221201012102111220001122011111
2010011110210022202222110201121222010021000202202020111222012101020101022102112221101110020120202011022211101212200220001212202200101202121221021211201202000122012021002110212020200101121120011022222
2001001101020110122000200122001001220010022022212120002021211001210022200201000210210120201222210221221102020100210200120211021101110000001011201210111210112101120011011020122222201120212200012122222
1002020002100220002101121200022222102212100001022222001120010200121111001100122000011020220112212122101222221010222012100020020121101212002110002201001121102022020101020222110012102001120211210022222
2121102022100000122100120020200100021112201200212201112021002221220021112121012011010200101011120211201210201101120102221201110221111021100021211102012121011112201202211112212221212110200000202100000
mindist=126
weight enumerator=1 [0]  2852 [126]  2610 [135]  1032 [144]  64 [153]  2 [162]

```
```q=3 k=12 n=221 d=129

(using automorphisms)

code with group 934

generator matrix:

00000000011111111111110001111111111111111111000011111111111111111100000000011111111111110000001111111111111111000000111111111111111100000001111111111111110000001111111111111111000000111111111111111100000011111111111111111
00000111100001111122221110000111222222222222000000000111111112222200111111100000001111220011110000111111122222000111000000011122222200111110000111111122220011110000011112222222001111000011111111222200111100111122222222220
01111012200120011212220021122012000111111122111101111000111220002200000111201112221112120100120012011122211222011022001112201200002201001221112111122202220101121222201221122222110122001101111122001211012212001200000011122
10222010102010122121222200102112011001112202002201222002011020120211022022120020121120211101001121100100101011102122121221111100220110012010220112202200011200001012201110000000002112020020011212110011020101122200112202200
01112222200100000221020201022002201021220102110110012112200101111001101001000220011211221200202221122112020011220122121011100102021111011010010011211111202120120200102010100112002100120210200112022102012120020202120220202
01221110101001202020201201010012202021122000121222020122112221210122120102200101210001000111000120212110122102101002100012211112222222010102211111022210021011222212211020211000010002020200000022111211200210212101001221122
21010001222111202100121021120022012201101110221210220011020010111222002010002202000120001100112222211201022212022200002200212212010021210202102201210102101102021000100210002221020222110211001121020212211011211202221222000
22210210100002020220120110122100202101221220110001011021010210202122021120200200102120020002102111010112010011101002011200012010210102102212020120010102102210220221021012101020120210111212221200001101112010021222101022200
00222102122112020202212021021120101221202101221122220112221112122101000111112011210222212222121222112100011222000122120200221100022222010002021202202122212121112210202112222022201122000102120022002200102121111210200100022
21202211210210020101121222220002212200122100021222211210001021110121121102222201211222022100222000102120022202000120210122201001201020020202121020211222211221111220001000102000121101222102211111011222221011002211112212100
00222001110000022010101211001002112021120212000200102011112120120002020112100022222001200100220002222200112110100102010021212221222200110222210201000200110202002202220011010222120121001020221101212112220211021110202021201
20020220211212011221021201202010001211111212222000100000001120022012021002110011000201220112210222001101012112201011222122101020011210022121200100100201010001222121112112202010112200120112021012111010212022202102100200021
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=129
weight enumerator=1 [0]  2970 [129]  11046 [132]  20394 [135]  38280 [138]  56936 [141]
79288 [144]  88528 [147]  84458 [150]  68684 [153]  43362 [156]  23342
[159]  10054 [162]  2838 [165]  990 [168]  220 [171]  44 [174]  6 [177
]

```

q=4

```q=4 k=7 n=181 d=128

(extension of a code)

generator matrix:
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[1,1]]
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[1,1]]
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mindist=128
weight enumerator=1 [0]  2925 [128]  4125 [132]  3633 [136]  3330 [140]  1680 [144]  465
[148]  225 [152]

```
```q=4 k=9 n=223 d=152

(extension of a code)

generator matrix:

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mindist=152
weight enumerator=1 [0]  4590 [152]  16779 [156]  35139 [160]  54060 [164]  59976 [168]
52584 [172]  27744 [176]  9384 [180]  1734 [184]  153 [188]

```
```q=4 k=9 n=229 d=156

(found by a program of Johannes Zwanzger)

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[0,0]]

mindist=156
weight enumerator=1 [0]  6300 [156]  13050 [160]  31230 [164]  36180 [168]  92250 [172]
39015 [176]  29973 [180]  8922 [184]  5220 [188]  3 [228]

```
```q=4 k=8 n=234 d=164

(extension of a code)

generator matrix:
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mindist=164
weight enumerator=1 [0]  5229 [164]  9849 [168]  12474 [172]  13608 [176]  13104 [180]  7821
[184]  2898 [188]  489 [192]  63 [196]

```
```q=4 k=9 n=234 d=160

(extension of a code)

generator matrix:

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mindist=160
weight enumerator=1 [0]  6705 [160]  15390 [164]  33840 [168]  32985 [172]  93510 [176]
37755 [180]  28128 [184]  8427 [188]  5400 [192]  3 [228]

```

q=5

```q=5 k=8 n=60 d=39

(using automorphisms)

code with group 128103

generator matrix:
000011111111000011111111001111111111000011111111000011111111
011100222344011122233344110011123344111101113444111111222224
114403134014101311312424110223342403001242234122003424011231
241414134224412304124020021244411213041233422114230101212333
244421334441021143121202241220314201211433324234220243232221
330222222204240143142433411311344021044432134321212240144340
244422431002020424204323313313432043230121400430301141424114
243433013330423114230014434442130044003414020231421124202334
corresponding to the solution:
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mindist=39
weight enumerator=1 [0]  1584 [39]  2640 [40]  4656 [41]  9280 [42]  14208 [43]  19776 [44
]  27856 [45]  37824 [46]  45024 [47]  51952 [48]  49488 [49]  44256 [50
]  33600 [51]  21840 [52]  14832 [53]  6992 [54]  3312 [55]  960 [56]
496 [57]  48 [58]

```
```q=5 k=8 n=76 d=51

(using automorphisms)

code with group 128103

generator matrix:
0001111111110011111111110011111111110111111111110011111111110111001111111111
0011111222240100112223441111222333341012222234440100112333441234110001111223
1100334003441124130034030224014334431420223410131312141344024342030121124024
0111340232202142322444131223123342424342024113414214042333440441104411343344
2221413233043221431144324242102220000440100210320331141303320201430412003423
2422103200342414420003403404003123201420313142431003141412310313312130212143
0144440304043124012113401100333441013210043100231220421324211340203231240124
1120414430433014402031140220413134002122423003321124320304201123034411241434
corresponding to the solution:
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mindist=51
weight enumerator=1 [0]  1664 [51]  3104 [52]  4128 [53]  8016 [54]  11024 [55]  16096 [56
]  23200 [57]  31584 [58]  35152 [59]  42304 [60]  45344 [61]  42400 [62
]  38048 [63]  33424 [64]  23024 [65]  14848 [66]  8736 [67]  4864 [68
]  2448 [69]  912 [70]  288 [71]  16 [73]

```

q=7

```q=7 k=6 n=71 d=54

(using automorphisms)

code with group 127895

generator matrix:
01111111011111110111111111111111001111111111100111111011111111111111110
10011566101334660001345602344666010255666034611001156111335554000223341
13503256020225461262265626001456134103364542102353301214251245134464413
43532041544125145600211245554251016123405246263602541114542520241500406
52515101455503161021014404361206432021605022666463426540350550203503366
50115221210261266321405506115140621346600266004135526425200063462540252
corresponding to the solution:
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mindist=54
weight enumerator=1 [0]  2088 [54]  3372 [55]  4500 [56]  6240 [57]  8892 [58]  12054 [59
]  14604 [60]  15432 [61]  13422 [62]  14172 [63]  10380 [64]  6888 [65
]  3768 [66]  1344 [67]  360 [68]  120 [69]  12 [70]

```

q=8

```q=8 k=5 n=123 d=102

(extension of a code)

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

mindist=102
weight enumerator=1 [0]  3157 [102]  6125 [104]  5635 [106]  6776 [108]  4802 [110]  3304
[112]  2163 [114]  658 [116]  147 [118]

```

q=9

University of Bayreuth -