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%I #7 Oct 04 2012 10:28:56
%S 1,1,1,1,2,1,1,1,2,7,1,1,1,3,13,3
%N Number of inequivalent codes attaining highest minimal distance of any Type I (strictly) singly-even binary self-dual code of length 2n.
%D J. H. Conway and V. S. Pless, On the enumeration of self-dual codes, J. Comb. Theory, A28 (1980), 26-53.
%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977.
%D V. S. Pless, The children of the (32,16) doubly even codes, IEEE Trans. Inform. Theory, 24 (1978), 738-746.
%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, A28 (1980), 26-53 (<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 P. Gaborit, <a href="http://www.unilim.fr/pages_perso/philippe.gaborit/SD/">Tables of Self-Dual Codes</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 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>).
%e At length 8 the only strictly Type I self-dual code is {00,11}^4, so a(4) = 1.
%Y Cf. A105674, A105675, A105676, A105677, A105678, A016729, A066016, A105681, A105682.
%Y A105674 gives the minimal distance of these codes, A106165 the number of codes of any minimal distance and A003179 the number of inequivalent codes allowing Type I or Type II and any minimal distance.
%K nonn
%O 1,5
%A _N. J. A. Sloane_, May 06 2005, Aug 23 2008
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