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Diskretn. Anal. Issled. Oper., 2014, Volume 21, Number 4, Pages 54–61 (Mi da785)  

This article is cited in 1 scientific paper (total in 1 paper)

Affine $3$-nonsystematic codes

S. A. Malyugin

S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: A perfect binary code $C$ of length $n=2^k-1$ is called affine $3$-systematic if in the space $\{0,1\}^n$ there exists a $3$-dimensional subspace $L$ such that the intersection of any of its cosets $L+u$ with the code $C$ is either empty or a singleton. Otherwise, the code $C$ is called affine $3$-nonsystematic. We construct affine $3$-nonsystematic codes of length $n=2^k-1$, $k\geq4$. Bibliogr. 11.

Keywords: perfect code, Hamming code, nonsystematic code, affine nonsystematic code, affine $3$-nonsystematic code, component.

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English version:
Journal of Applied and Industrial Mathematics, 2014, 8:4, 552–556

Bibliographic databases:

UDC: 519.8
Received: 23.12.2013
Revised: 17.01.2014

Citation: S. A. Malyugin, “Affine $3$-nonsystematic codes”, Diskretn. Anal. Issled. Oper., 21:4 (2014), 54–61; J. Appl. Industr. Math., 8:4 (2014), 552–556

Citation in format AMSBIB
\Bibitem{Mal14}
\by S.~A.~Malyugin
\paper Affine $3$-nonsystematic codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2014
\vol 21
\issue 4
\pages 54--61
\mathnet{http://mi.mathnet.ru/da785}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3289221}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 4
\pages 552--556
\crossref{https://doi.org/10.1134/S1990478914040127}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Malyugin, “Affine $3$-nonsystematic perfect codes of length 15”, J. Appl. Industr. Math., 9:2 (2015), 251–262  mathnet  crossref  crossref  mathscinet  elib
  • Дискретный анализ и исследование операций
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