Database of Binary Self-Dual Codes

Length	#	Data	Remarks
2	1	2.magma	all
4	1	4.magma	all
6	1	6.magma	all
8	2	8-I.magma 8-II.magma	type I (unique) type II (unique)
10	2	10.magma	all
12	3	12.magma	all
14	4	14.magma	all
16	7	16-I.magma 16-II.magma	type I (5 codes) type II (2 codes)
18	9	18.magma	all
20	16	20.magma	all
22	25	22.magma	all
24	55	24-I.magma 24-II.magma	type I (46 codes) type II (9 codes)
26	103	26.magma	all
28	261	28.magma	all
30	731	30.magma	all
32	3295	32-I.magma 32-II.magma	type I (3210 codes) type II (85 codes)
34	24147	34.magma	all
36	519492	36-d2.magma 36-d4-1.magma 36-d4-2.magma 36-d4-3.magma 36-d4-4.magma 36-d4-5.magma 36-d4-6.magma 36-d4-7.magma 36-d4-8.magma 36-d4-9.magma 36-d6.magma 36-d8.magma	minimum weight 2 (24147 codes) minimum weight 4 (part 1) minimum weight 4 (part 2) minimum weight 4 (part 3) minimum weight 4 (part 4) minimum weight 4 (part 5) minimum weight 4 (part 6) minimum weight 4 (part 7) minimum weight 4 (part 8) minimum weight 4 (part 9) (total 436633 codes) minimum weight 6 (58671 codes) minimum weight 8 (41 codes)
38	38682183	38-d8.magma.gz	minimum weight 8 (2744 codes)
40		40-I-beta0.tar.gz 40-I-beta1.tar.gz 40-I-beta2.magma.gz 40-I-beta3.magma.gz 40-I-beta4.magma.gz 40-I-beta5.magma.gz 40-I-beta6.magma.gz 40-I-beta7.magma 40-I-beta8.magma 40-I-beta10.magma 40-II8.magma 40-II-d4.magma.gz	type I, minimum weight 8, beta=0 (3597997 codes) type I, minimum weight 8, beta=1 (4674608 codes) type I, minimum weight 8, beta=2 (1511827 codes) type I, minimum weight 8, beta=3 (337565 codes) type I, minimum weight 8, beta=4 (64692 codes) type I, minimum weight 8, beta=5 (11009 codes) type I, minimum weight 8, beta=6 (2413 codes) type I, minimum weight 8, beta=7 (405 codes) type I, minimum weight 8, beta=8 (120 codes) type I, minimum weight 8, beta=10 (19 codes) type II, minimum weight 8 (16470 codes) type II, minimum weight 4 (77873 codes) (\beta means the number of weight 4 words in the shadow)

Data files are in Magma format.

The data for length 36 are very large, so they are split into nine parts. It may take five hours and 2GB of memory to load them all.

Magma programs

checking equivalence and mass formula (for lengths up to 34): program
cheking equivalence and mass formula (for length 40, minimum weight 8): program

References

[Length 2-20] V. Pless, A classification of self-orthogonal codes over GF(2), Discrete Math. 3 (1972), 209-246.
[Length 22-24] V. Pless and N. J. A. Sloane, On the classification and enumeration of self-dual codes, J. Combinatorial Theory Ser. A 18 (1975), 313-335.
[Length 26-30, 32 (type II)] J. H. Conway, V. Pless and N. J. A. Sloane, The binary self-dual codes of length up to 32: a revised enumeration, J. Combin. Theory Ser. A 60 (1992), 183-195.
[Length 32 (type I)] R. T. Bilous and G. H. J. van Rees, An enumeration of binary self-dual codes of length 32, Des. Codes Cryptogr. 26 (2002), 61-86.
[Length 34] R. T. Bilous, Enumeration of the binary self-dual codes of length 34, J. Combin. Math. Combin. Comput. 59 (2006), 173-211.
[Length 36] M. Harada and A. Munemasa, Classification of self-dual codes of length 36, Advances Math. Communications 6 (2012), 229-235.
[Length 38 (minimum weight 8)] C. Aguilar-Melchor, P. Gaborit, J.-L. Kim, L. Sok and P. Sole, Classification of extremal and s-extremal binary self-dual codes of length 38, IEEE Trans. Inform. Theory 58 (2012), 2253-2262.
[Length 38 (minimum weight 8), 40 (type II)] K. Betsumiya, M. Harada and A. Munemasa, A complete classification of doubly even self-dual codes of length 40, Electronic J. Combin. 19 (2012), #P18 (12 pp.).
[Length 38] S. Bouyuklieva and I. Bouyukliev, An algorithm for classification of binary self-dual codes, IEEE Trans. Inform. Theory 58 (2012), 3933-3940.
[Length 40 (type I, minimum weight 8)] S. Bouyuklieva, I. Bouyukliev and M. Harada, Some extremal self-dual codes and unimodular lattices in dimension 40, Finite Fields and Their Applications 21 (2013), 67-83.

Created November 15, 2007 by Masaaki Harada and Akihiro Munemasa
Last modified May 1, 2013.