Database of self-dual codes of short lengths

Classification of self-dual Z_k-codes C with A_k(C) ≅ L

k \L	Z	Z²	Z³	Z⁴	Z⁵	Z⁶	Z⁷	Z⁸	E₈	Z⁹	E₈⊕ Z⁸
2	0	1	0	1	0	1	0	1	1	0	0
3	0	0	0	1	0	0	0	1	0	0	0
4	1	1	1	2	2	3	4	7	4	7	4
5	0	1	0	1	0	2	0	3	0	0	0
6	0	0	0	1	0	0	0	3	2	0	0
7	0	0	0	1	0	0	0	4	0	0	0
8	0	1	0	1	0	3	0	20	9	0	0
9	1	1	2	3	3	6	9	16	0	28	7
10	0	1	0	2	0	5	0	16	11	0	0
11	0	0	0	1	0	0	0	8	0	0	0
12	0	0	0	2	0	0	0	73	22	0	0
13	0	1	0	2	0	5	0	21	0	0	0
14	0	0	0	1	0	0	0	27	18	0	0
15	0	0	0	2	0	0	0	51	0	0	0
16	1	1	1	2	3	7	23	295	63	697	141
17	0	1	0	2	0	6	0	47	0	0	0
18	0	1	0	4	0	12	0	178	69	0	0
19	0	0	0	2	0	0	0	57	0	0	0
20	0	1	0	2	0	17	0	725	176	0	0
21	0	0	0	3	0	0	0	208	0	0	0
22	0	0	0	2	0	0	0	166	75	0	0
23	0	0	0	1	0	0	0	120	0	0	0
24	0	0	0	1	0	0	0	3690	456	0	0

Data files are in Magma format.

Magma programs

checking equivalence
checking mass formula
extracting codes from a lattice

References

M. Harada and A. Munemasa, On the classification of self-dual Z_k-codes II, (preprint in arXiv).

Links

Markus Grassl
"Bounds on the minimum distance of linear codes"
http://www.codetables.de
Philippe Gaborit and Ayoub Otmani
"Tables of self-dual codes"
N.J.A. Sloane,
"A library of linear (and nonlinear) codes "

Created May 24, 2009 by Masaaki Harada and Akihiro Munemasa
Last modified October 16, 2018.