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Divisible Linear Codes
Table 4. Even binary codes with n ≤ 20, k ≤ 10, $d ≥ 6 codes. 20_10_6.2bh_pri
n\k |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
9 |
1 |
|
|
|
|
|
|
|
|
10 |
1 |
|
|
|
|
|
|
|
|
11 |
2 |
1 |
|
|
|
|
|
|
|
12 |
3 |
4 |
1 |
|
|
|
|
|
|
13 |
3 |
6 |
4 |
|
|
|
|
|
|
14 |
4 |
15 |
18 |
5 |
|
|
|
|
|
15 |
5 |
23 |
62 |
46 |
5 |
|
|
|
|
16 |
6 |
41 |
168 |
328 |
120 |
3 |
|
|
|
17 |
6 |
55 |
402 |
1713 |
2489 |
329 |
1 |
|
|
18 |
8 |
89 |
891 |
7400 |
31438 |
28863 |
907 |
1 |
|
19 |
8 |
114 |
1775 |
26383 |
269928 |
970102 |
416439 |
1694 |
|
20 |
10 |
168 |
3397 |
83672 |
1771843 |
17927353 |
39994046 |
5707389 |
1681 |
total |
57 |
516 |
6718 |
119547 |
2075823 |
18926650 |
40411393 |
5709084 |
1681 |
Table 5. Even binary codes with n ≤ 18, k ≤ 12, d ≥ 4. 18_12_4.2bh_pri
n\k |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
6 |
1 |
|
|
|
|
|
|
|
|
|
|
7 |
1 |
1 |
|
|
|
|
|
|
|
|
|
8 |
2 |
2 |
1 |
|
|
|
|
|
|
|
|
9 |
2 |
3 |
2 |
|
|
|
|
|
|
|
|
10 |
3 |
8 |
9 |
3 |
|
|
|
|
|
|
|
11 |
3 |
10 |
18 |
11 |
2 |
|
|
|
|
|
|
12 |
5 |
21 |
50 |
55 |
19 |
2 |
|
|
|
|
|
13 |
4 |
25 |
96 |
172 |
115 |
21 |
1 |
|
|
|
|
14 |
6 |
43 |
207 |
582 |
703 |
272 |
28 |
1 |
|
|
|
15 |
6 |
53 |
378 |
1659 |
3569 |
2734 |
567 |
28 |
1 |
|
|
16 |
8 |
83 |
722 |
4730 |
17377 |
26214 |
11891 |
1263 |
36 |
1 |
|
17 |
7 |
98 |
1240 |
12338 |
77834 |
225761 |
220180 |
54039 |
2614 |
29 |
|
18 |
10 |
145 |
2200 |
31848 |
335287 |
1828735 |
3707982 |
2117150 |
263147 |
5568 |
30 |
total |
58 |
492 |
4923 |
51398 |
434906 |
2083739 |
3940649 |
2172481 |
265798 |
5598 |
30 |
Table 6. Divisible ternary codes with n ≤ 50, k ≤ 6 and Delta=9. 50_6_9.3bh_prin
n\k |
2 |
3 |
4 |
5 |
6 |
12 |
1 |
|
|
|
|
13 |
|
1 |
|
|
|
18 |
1 |
|
|
|
|
21 |
1 |
1 |
|
|
|
22 |
|
1 |
1 |
|
|
24 |
1 |
1 |
1 |
|
|
25 |
|
1 |
1 |
1 |
|
26 |
|
1 |
1 |
1 |
1 |
27 |
2 |
3 |
3 |
1 |
|
30 |
2 |
4 |
3 |
|
|
31 |
|
2 |
3 |
1 |
|
33 |
1 |
5 |
5 |
3 |
|
34 |
|
2 |
5 |
4 |
1 |
35 |
|
1 |
4 |
4 |
3 |
36 |
4 |
10 |
22 |
13 |
4 |
37 |
|
2 |
7 |
10 |
3 |
38 |
|
1 |
6 |
12 |
10 |
39 |
3 |
15 |
34 |
41 |
23 |
40 |
|
6 |
25 |
40 |
30 |
42 |
2 |
17 |
52 |
44 |
15 |
43 |
|
6 |
32 |
40 |
16 |
44 |
|
2 |
14 |
22 |
17 |
45 |
5 |
31 |
141 |
190 |
72 |
46 |
|
6 |
56 |
122 |
71 |
47 |
|
2 |
29 |
92 |
89 |
48 |
5 |
44 |
297 |
705 |
468 |
49 |
|
15 |
177 |
613 |
596 |
50 |
|
2 |
39 |
217 |
295 |
total |
28 |
182 |
958 |
2176 |
1714 |
Table 7. Divisible quaternary codes with n ≤ 30, k ≤ 8 and Delta=4. 30_8_4.4h_print
n\k |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
5 |
1 |
|
|
|
|
|
|
8 |
1 |
|
|
|
|
|
|
9 |
1 |
1 |
|
|
|
|
|
10 |
1 |
1 |
1 |
|
|
|
|
12 |
2 |
2 |
|
|
|
|
|
13 |
2 |
3 |
1 |
|
|
|
|
14 |
1 |
5 |
3 |
1 |
|
|
|
15 |
1 |
3 |
6 |
2 |
1 |
|
|
16 |
4 |
9 |
7 |
2 |
|
|
|
17 |
3 |
12 |
9 |
2 |
|
|
|
18 |
2 |
18 |
25 |
8 |
1 |
|
|
19 |
1 |
14 |
42 |
25 |
6 |
1 |
|
20 |
6 |
34 |
93 |
70 |
22 |
4 |
1 |
21 |
5 |
45 |
115 |
75 |
19 |
2 |
|
22 |
3 |
64 |
245 |
131 |
23 |
2 |
|
23 |
2 |
62 |
554 |
398 |
96 |
12 |
1 |
24 |
9 |
123 |
1509 |
1769 |
491 |
79 |
9 |
25 |
|
168 |
3189 |
6890 |
1842 |
334 |
46 |
26 |
|
|
8420 |
18377 |
2691 |
360 |
33 |
27 |
|
|
|
70147 |
4602 |
458 |
34 |
28 |
|
|
|
|
36982 |
3075 |
244 |
29 |
|
|
|
|
|
34180 |
2366 |
30 |
|
|
|
|
|
|
24565 |
total |
45 |
564 |
14219 |
97897 |
46776 |
38507 |
27299 |
Table 8. Doubly even binary codes of length n ≤ 32 and dimension k ≤ 6. 32_6_4.2bh_prin
n\k |
2 |
3 |
4 |
5 |
6 |
6 |
1 |
|
|
|
|
7 |
|
1 |
|
|
|
8 |
1 |
1 |
1 |
|
|
10 |
1 |
1 |
1 |
|
|
11 |
|
1 |
1 |
|
|
12 |
2 |
3 |
4 |
2 |
|
13 |
|
1 |
1 |
2 |
|
14 |
2 |
4 |
6 |
5 |
4 |
15 |
|
3 |
6 |
6 |
4 |
16 |
3 |
8 |
18 |
21 |
15 |
17 |
|
2 |
7 |
14 |
11 |
18 |
3 |
9 |
27 |
44 |
45 |
19 |
|
6 |
22 |
52 |
62 |
20 |
4 |
17 |
64 |
149 |
212 |
21 |
|
6 |
36 |
144 |
276 |
22 |
4 |
20 |
104 |
373 |
852 |
23 |
|
12 |
89 |
475 |
1489 |
24 |
6 |
34 |
220 |
1157 |
4317 |
25 |
|
12 |
148 |
1364 |
7890 |
26 |
5 |
39 |
359 |
3115 |
22278 |
27 |
|
22 |
321 |
4397 |
49390 |
28 |
7 |
61 |
701 |
9492 |
137980 |
29 |
|
24 |
557 |
13421 |
330979 |
30 |
7 |
72 |
1173 |
27638 |
921270 |
31 |
|
41 |
1106 |
42656 |
2374543 |
32 |
9 |
106 |
2163 |
84258 |
6556687 |
total |
55 |
506 |
7135 |
188785 |
10408304 |