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

0, 1, 1, 1, 2, 2, 3, 5, 7, 10, 17, 29, 58, 113, 274, 772, 3361

Offset: 1

Author

Nathan J. Russell, Dec 07 2018

Keywords

• nonn
• more

Comments

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.

Examples

			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.
		

Links

• 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.
• W. Cary Huffman and Vera Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003, pp. 7, 18, 338-393.
• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
• 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.

Formula

a(n) = A003179(n) - A003178(n).