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An upper bound for the number of uniformly packed binary codes

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Abstract

Under study are the binary codes uniformly packed (in the wide sense) of length n with minimum distance d and covering radius ρ. It is shown that every code of this kind is uniquely determined by the set of its codewords of weights ⌈n/2⌉ − ρ, …, ⌊n/2⌋ + ρ. For odd d, the number of distinct codes is at most

$$ 2^{2^{n - \tfrac{3} {2}\log n + o(log n)} } $$

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    N. N. Tokareva

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  1. N. N. Tokareva
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Correspondence to N. N. Tokareva.

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Original Russian Text © N.N. Tokareva, 2007, published in Diskretnyi Analiz i Issledovanie Operatsii, Ser. 1, 2007, Vol. 14, No. 3, pp. 90–97.

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Tokareva, N.N. An upper bound for the number of uniformly packed binary codes. J. Appl. Ind. Math. 2, 426–431 (2008). https://doi.org/10.1134/S1990478908030137

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  • DOI: https://doi.org/10.1134/S1990478908030137

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