A105674 - OEIS

%I #12 Oct 08 2023 04:42:46

%S 2,2,2,2,2,4,4,4,4,4,6,6,6,6,6,8,6,8,8,8,8,8,10,10,10,10,10

%N Highest minimal distance of any Type I (strictly) singly-even binary self-dual code of length 2n.

%C The sequence continues: a(28) = either 10 or 12, then a(58) = 10, a(60) through a(68) = 12, ...

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977.

%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 P. Gaborit, <a href="http://www.unilim.fr/pages_perso/philippe.gaborit/SD/">Tables of Self-Dual Codes</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>).

%e At length 8 the only strictly Type I self-dual code is {00,11}^4, which has d=2, so a(4) = 2.

%Y Cf. A105675, A105676, A105677, A105678, A016729, A066016, A105681, A105682.

%Y Cf. also A105685 for the number of such codes.

%K nonn,nice,more

%O 1,1

%A _N. J. A. Sloane_, May 06 2005