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On the admissible families of components of hamming codes

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Abstract

In this paper, the properties of the i-components of Hamming codes are described. We suggest constructions of the admissible families of components of Hamming codes. Each q-ary code of length m and minimum distance 5 (for q = 3, the minimum distance is 3) is shown to embed in a q-ary 1-perfect code of length n = (q m − 1)/(q − 1). Moreover, each binary code of length m+k and minimum distance 3k + 3 embeds in a binary 1-perfect code of length n = 2m − 1.

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References

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

    A. M. Romanov

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  1. A. M. Romanov
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Correspondence to A. M. Romanov.

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Original Russian Text © A.M. Romanov, 2012, published in Diskretnyi Analiz i Issledovanie Operatsii, 2012, Vol. 19, No. 2, pp. 85–92.

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Romanov, A.M. On the admissible families of components of hamming codes. J. Appl. Ind. Math. 6, 355–359 (2012). https://doi.org/10.1134/S1990478912030106

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  • DOI: https://doi.org/10.1134/S1990478912030106

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