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A322429
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Number of decomposable binary self-dual codes of length 2n (up to permutation equivalence).
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1
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0, 1, 1, 1, 2, 2, 3, 5, 7, 10, 17, 29, 58, 113, 274, 772, 3361
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OFFSET
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1,5
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COMMENTS
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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.
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LINKS
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E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).
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FORMULA
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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