A106163 Total number of (indecomposable or decomposable) Type II binary self-dual codes of length 8n.

1, 1, 2, 9, 85, 94343

Offset

0,3

Comments

"There are 94343 inequivalent doubly even self-dual codes of length 40, 16470 of which are extremal" [Betsumiya et al.] - Jonathan Vos Post, Aug 06 2012

Links

Table of n, a(n) for n=0..5.

Koichi Betsumiya, Masaaki Harada and Akihiro Munemasa, A Complete Classification of Doubly Even Self-Dual Codes of Length 40, arXiv:1104.3727v3 [math.CO], v3, Aug 02, 2012. - From Jonathan Vos Post, Aug 06 2012

J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53. [DOI] MR0558873

J. H. Conway, V. Pless and N. J. A. Sloane, The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration, J. Comb. Theory, A60 (1992), 183-195 (Abstract, pdf, ps, Table A, Table D).

W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic. 11 (2005), 451-490. [DOI]

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746. [DOI] MR0514353

E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).

Crossrefs

Cf. A003178, A003179, A106162, A106163, A106164, A106165, A106166, A106167, A215219.

Sequence in context: A330475 A356615 A037172 * A368186 A359903 A360433

Adjacent sequences: A106160 A106161 A106162 * A106164 A106165 A106166

Keyword

nonn,hard,more

Author

N. J. A. Sloane, May 09 2005

Status

approved