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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 |