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

1,5

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.

Links

Table of n, a(n) for n=1..17.

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).

Formula

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

Example

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.

Crossrefs

Cf. A003178, A003179.

Sequence in context: A120412 A022864 A316075 * A039894 A133225 A240487

Adjacent sequences: A322426 A322427 A322428 * A322430 A322431 A322432

Keyword

nonn,more

Author

Nathan J. Russell, Dec 07 2018

Status

approved