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Self-orthogonal codes
Table 1. Classification of binary self-orthogonal codes.
| n\k |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| 7 |
4 1 |
|
|
|
|
|
|
|
| 8 |
4 1 |
4 1 |
|
|
|
|
|
|
| 9 |
4 1 |
4 0 |
|
|
|
|
|
|
| 10 |
4 3 |
4 3 |
|
|
|
|
|
|
| 11 |
4 2 |
4 2 |
4 1 |
|
|
|
|
|
| 12 |
6 1 |
4 10 |
4 5 |
4 1 |
|
|
|
|
| 13 |
6 1 |
4 6 |
4 5 |
4 1 |
|
|
|
|
| 14 |
8 1 |
6 2 |
4 22 |
4 10 |
4 1 |
|
|
|
| 15 |
8 1 |
8 1 |
6 1 |
4 13 |
4 3 |
|
|
|
| 16 |
8 3 |
8 2 |
8 1 |
6 1 |
4 20 |
4 3 |
|
|
| 17 |
8 3 |
8 2 |
8 1 |
6 2 |
4 37 |
4 4 |
|
|
| 18 |
8 8 |
8 10 |
8 5 |
8 2 |
6 3 |
4 45 |
4 2 |
|
| 19 |
10 1 |
8 12 |
8 10 |
8 2 |
8 1 |
6 1 |
4 12 |
|
| 20 |
10 2 |
8 50 |
8 50 |
8 23 |
8 4 |
8 1 |
6 1 |
4 7 |
| 21 |
12 1 |
10 1 |
8 101 |
8 57 |
8 15 |
8 2 |
8 1 |
6 1 |
| 22 |
12 1 |
10 6 |
8 417 |
8 416 |
8 117 |
8 16 |
8 2 |
8 1 |
| 23 |
12 3 |
12 1 |
10 2 |
8 1729 |
8 848 |
8 104 |
8 12 |
8 2 |
| 24 |
12 6 |
12 4 |
12 1 |
10 1 |
8 9839 |
8 1824 |
8 124 |
8 16 |
| 25 |
12 8 |
12 6 |
12 2 |
10 27 |
8 96560 |
8 37625 |
8 1891 |
8 60 |
| 26 |
14 1 |
12 27 |
12 13 |
12 2 |
10 26 |
8 |
8 |
8 1689 |
| 27 |
14 2 |
12 48 |
12 60 |
12 24 |
12 1 |
10 1 |
8 |
8 |
| 28 |
16 1 |
14 1 |
12 345 |
12 383 |
12 61 |
10 43579 |
8 |
8 |
| 29 |
16 1 |
14 3 |
12 1507 |
12 4468 |
12 5694 |
12 73 |
10 |
8 |
| 30 |
16 3 |
16 1 |
14 3 |
12 |
12 |
12 |
12 9 |
10 |
| 31 |
16 6 |
16 2 |
16 1 |
12 |
12 |
12 |
12 |
12 2 |
| 32 |
16 12 |
16 9 |
16 3 |
16 1 |
12 |
12 |
12 |
12 |
| 33 |
18 1 |
16 16 |
16 8 |
16 0 |
12 |
12 |
12 |
12 |
| 34 |
18 2 |
16 71 |
16 63 |
16 15 |
14 5399 |
12 |
12 |
12 |
| 35 |
20 1 |
16 152 |
16 380 |
16 362 |
16 4 |
14 |
12 |
12 |
| 36 |
20 1 |
18 2 |
16 2876 |
16 20392 |
16 7484 |
16 2 |
14 |
12 |
| 37 |
20 3 |
18 8 |
16 17705 |
16 |
16 |
16 |
14 |
14 |
| 38 |
20 6 |
20 1 |
18 3 |
16 |
16 |
16 |
16 47 |
14 |
| 39 |
20 12 |
20 4 |
18 50 |
16 |
16 |
16 |
16 |
14 |
| 40 |
22 1 |
20 17 |
20 3 |
18 41 |
16 |
16 |
16 |
16 |
Table 2. Classification of ternary self-orthogonal codes.
| n\k |
3 |
4 |
5 |
6 |
| 7 |
3 1 |
|
|
|
| 8 |
3 1 |
3 1 |
|
|
| 9 |
6 1 |
3 1 |
|
|
| 10 |
6 1 |
6 1 |
|
|
| 11 |
6 2 |
6 1 |
6 1 |
|
| 12 |
6 6 |
6 6 |
6 1 |
6 1 |
| 13 |
9 1 |
6 10 |
6 4 |
6 1 |
| 14 |
9 1 |
6 27 |
6 15 |
6 4 |
| 15 |
9 4 |
9 3 |
6 73 |
6 20 |
| 16 |
9 9 |
9 13 |
9 1 |
6 121 |
| 17 |
9 16 |
9 58 |
9 35 |
6 885 |
| 18 |
12 2 |
9 308 |
9 997 |
9 105 |
| 19 |
12 4 |
12 1 |
9 15207 |
9 18019 |
| 20 |
12 14 |
12 32 |
12 2 |
9 |
| 21 |
12 36 |
12 406 |
12 359 |
9 |
| 22 |
15 1 |
12 3679 |
12 107017 |
12 698 |
| 23 |
15 3 |
12 20673 |
12 |
12 |
| 24 |
15 15 |
15 13 |
12 |
12 |
| 25 |
18 45 |
15 699 |
15 23 |
12 |
| 26 |
18 1 |
15 17703 |
15 |
15 2 |
| 27 |
18 4 |
18 1 |
15 |
15 |
| 28 |
18 14 |
18 6 |
15 |
15 |
| 29 |
18 49 |
18 406 |
18 1 |
15 |
Table 3. Classification of Hermitian self-orthogonal codes over F4.
| n\k |
3 |
4 |
5 |
6 |
| 6 |
4 1 |
|
|
|
| 7 |
4 1 |
|
|
|
| 8 |
4 4 |
4 1 |
|
|
| 9 |
6 1 |
4 2 |
|
|
| 10 |
6 4 |
4 12 |
4 2 |
|
| 11 |
6 6 |
6 2 |
4 6 |
|
| 12 |
8 5 |
6 22 |
6 2 |
4 5 |
| 13 |
8 10 |
8 5 |
6 19 |
6 1 |
| 14 |
10 1 |
8 92 |
8 4 |
6 23 |
| 15 |
10 7 |
8 911 |
8 460 |
8 3 |
| 16 |
12 1 |
10 50 |
8 45311 |
8 1081 |
| 17 |
12 4 |
12 1 |
10 91 |
8 |
| 18 |
12 45 |
12 12 |
10 |
10 3 |
| 19 |
12 185 |
12 5673 |
10 |
10 |
| 20 |
14 10 |
12 |
12 |
10 |
| 21 |
16 1 |
14 212 |
12 |
12 |
| 22 |
16 4 |
14 |
14 67 |
12 |
| 23 |
16 46 |
16 3 |
14 |
12 |
| 24 |
16 614 |
16 40397 |
16 |
14 |
| 25 |
18 6 |
16 |
16 |
14 |
| 26 |
18 185 |
18 14 |
16 |
16 |
| 27 |
20 2 |
18 |
16 |
16 |
| 28 |
20 46 |
20 1 |
18 |
16 |
| 29 |
20 850 |
20 22656 |
18 |
16 |
REFERENCES