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Self-orthogonal Codes




Table 1. Classification of binary self orthogonal codes with n ≤ 27,k ≤ 12 and d ≥ 8. 27_12_8.2bh_pri

n\k 2 3 4 5 6 7 8 9 10 11 12
12 1
14 2 1
15 1 1
16 4 3 2 1
17 3 2 1
18 6 8 10 5 2
19 8 12 10 2 1
20 8 21 50 50 23 4 1
21 15 53 101 57 15 2 1
22 10 41 175 417 416 117 16 2 1
23 27 197 925 1729 848 104 12 2 1
24 13 76 539 3070 10043 9839 1824 124 16 3 1
25 45 589 6403 41905 96560 37625 1891 60 6
26 15 125 1425 17948 191021 936415 990557 107917 1689 50 6
27 71 1560 35784 714335 7470965 20226632 6920973 158046 731 11
total 59 445 4615 64715 959533 8514764 21256761 7030920 159814 791 18


Table 2. Classification of ternary self-orthogonal codes with n ≤ 20, k ≤ 12, $d ≥ 6.   20_12_6.3bh_pri

n\k 2 3 4 5 6 7 8 9 10
8 1
9 1 1
10 1 1 1
11 1 2 1 1
12 3 6 6 2 1
13 2 8 10 4 1
14 2 12 27 15 4
15 4 23 78 73 20 2
16 4 32 181 312 121 11 1
17 3 45 414 1466 885 86 2
18 7 79 1097 8103 10808 1401 40
19 5 107 2589 47015 167786 45950 1132 10
20 5 146 6484 285428 2851808 2121360 89670 464 6
total 39 462 10888 342419 3031434 2168810 90845 474 6


Table 3. Quaternary Hermitian self-orthogonal codes with n ≤ 21, k ≤ 6 and d ≥ 12 21_6_12.4h_prin

n\k 2 3 4 5 6
15 1
16 2 1
17 3 4 1
18 45 12
19 5673
20 886576
21 577008
total 6 50 5686 886576 577008