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On switching equivalence of n-ary quasigroups of order 4 and perfect binary codes

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Abstract

We prove that arbitrary n-ary quasigroups of order 4 can be transformed into each other by successive switchings of {a, b}-components. We prove that perfect (closely packed) binary codes with distance 3 whose rank (dimension of the linear span) is greater by 1 or 2 than the rank of a linear perfect code can be taken to each other by successive switchings of i-components.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk Novosibirsk State University, Novosibirsk, Russia

    D. S. Krotov & V. N. Potapov

Authors
  1. D. S. Krotov
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  2. V. N. Potapov
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Correspondence to D. S. Krotov.

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Original Russian Text © D.S. Krotov, V.N. Potapov, 2010, published in Problemy Peredachi Informatsii, 2010, Vol. 46, No. 3, pp. 22–28.

Supported in part by the Federal Target Program “Research and Educational Personnel of Innovation Russia” for 2009–2013, government contract no. 02.740.11.0429, and Russian Foundation for Basic Research, project nos. 10-01-00424 and 10-01-00616.

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Krotov, D.S., Potapov, V.N. On switching equivalence of n-ary quasigroups of order 4 and perfect binary codes. Probl Inf Transm 46, 219–224 (2010). https://doi.org/10.1134/S0032946010030026

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  • DOI: https://doi.org/10.1134/S0032946010030026

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