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A322429 Number of decomposable binary self-dual codes of length 2n (up to permutation equivalence). 1
0, 1, 1, 1, 2, 2, 3, 5, 7, 10, 17, 29, 58, 113, 274, 772, 3361 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A120412 A022864 A316075 * A039894 A133225 A240487
KEYWORD
nonn,more
AUTHOR
Nathan J. Russell, Dec 07 2018
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)