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Probl. Peredachi Inf., 2010, Volume 46, Issue 3, Pages 22–28 (Mi ppi2019)  

This article is cited in 3 scientific papers (total in 3 papers)

Coding Theory

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

D. S. Krotovab, V. N. Potapovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University

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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English version:
Problems of Information Transmission, 2010, 46:3, 219–224

Bibliographic databases:

Document Type: Article
UDC: 621.391.15+519.7
Received: 06.11.2009
Revised: 14.05.2010

Citation: D. S. Krotov, V. N. Potapov, “On switching equivalence of $n$-ary quasigroups of order 4 and perfect binary codes”, Probl. Peredachi Inf., 46:3 (2010), 22–28; Problems Inform. Transmission, 46:3 (2010), 219–224

Citation in format AMSBIB
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\pages 22--28
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\pages 219--224
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Potapov, “Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes”, Problems Inform. Transmission, 48:1 (2012), 47–55  mathnet  crossref  isi
    2. D. I. Kovalevskaya, F. I. Solov'eva, E. S. Filimonova, “Steiner triple systems of small rank embedded into perfect binary codes”, J. Appl. Industr. Math., 7:3 (2013), 380–395  mathnet  crossref  mathscinet
    3. D. I. Kovalevskaya, F. I. Solov'eva, “Steiner quadruple systems of small ranks and extended perfect binary codes”, J. Appl. Industr. Math., 7:4 (2013), 522–536  mathnet  crossref  mathscinet
  • Проблемы передачи информации Problems of Information Transmission
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