%I #23 May 29 2014 05:16:25

%S 1,1,2,9,85,94343

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

%C "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

%H Koichi Betsumiya, Masaaki Harada and Akihiro Munemasa, <a href="http://arxiv.org/abs/1104.3727">A Complete Classification of Doubly Even Self-Dual Codes of Length 40</a>, arXiv:1104.3727v3 [math.CO], v3, Aug 02, 2012. - From _Jonathan Vos Post_, Aug 06 2012

%H J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53. <a href="http://dx.doi.org/10.1016/0097-3165(80)90057-6">[DOI]</a> <a href="http://www.ams.org/mathscinet-getitem?mr=558873">MR0558873</a>

%H 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 (<a href="http://neilsloane.com/doc/pless.txt">Abstract</a>, <a href="http://neilsloane.com/doc/pless.pdf">pdf</a>, <a href="http://neilsloane.com/doc/pless.ps">ps</a>, <a href="http://neilsloane.com/doc/plesstaba.ps">Table A</a>, <a href="http://neilsloane.com/doc/plesstabd.ps">Table D</a>).

%H W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic. 11 (2005), 451-490. <a href="http://dx.doi.org/10.1016/j.ffa.2005.05.012">[DOI]</a>

%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.

%H V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746. <a href="http://dx.doi.org/10.1109/TIT.1978.1055966">[DOI]</a> <a href="http://www.ams.org/mathscinet-getitem?mr=514353">MR0514353</a>

%H E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (<a href="http://neilsloane.com/doc/self.txt">Abstract</a>, <a href="http://neilsloane.com/doc/self.pdf">pdf</a>, <a href="http://neilsloane.com/doc/self.ps">ps</a>).

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

%K nonn,hard,more

%O 0,3

%A _N. J. A. Sloane_, May 09 2005