cp's OEIS Frontend

A322429 Number of decomposable binary self-dual codes of length 2n (up to permutation equivalence).

%I A322429 #10 Dec 10 2018 14:13:02
%S A322429 0,1,1,1,2,2,3,5,7,10,17,29,58,113,274,772,3361
%N A322429 Number of decomposable binary self-dual codes of length 2n (up to permutation equivalence).
%C A322429 Every binary self-dual code is either indecomposable or decomposable.  A decomposable binary self-dual code is the direct sum of a set of indecomposable binary self-dual codes of smaller length.
%H A322429 J. H. Conway, V. Pless and N. J. A. Sloane, <a href="https://doi.org/10.1016/0097-3165(92)90003-D">The Binary Self-Dual Codes of Length Up to 32: A Revised Enumeration</a>, J. Comb. Theory, A28 (1980), 26-53.
%H A322429 W. Cary Huffman and Vera Pless, <a href="https://doi.org/10.1017/CBO9780511807077">Fundamentals of Error Correcting Codes</a>, Cambridge University Press, 2003, pp. 7, 18, 338-393.
%H A322429 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 A322429 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>).
%F A322429 a(n) = A003179(n) - A003178(n).
%e A322429 There are A003179(17) = 24147 binary self-dual codes of length 2*17 = 34 up to permutation equivalence.  There are A003178(17) = 2523 binary self-dual codes of length 2*17 = 34 that are indecomposable.  This means that there are A003179(17) - A003178(17) = a(17) = 3361 binary self-dual codes of length 2*17=34 that are decomposable.
%Y A322429 Cf. A003178, A003179.
%K A322429 nonn,more
%O A322429 1,5
%A A322429 _Nathan J. Russell_, Dec 07 2018