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Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 4, Pages 73–85 (Mi da699)  

This article is cited in 2 scientific papers (total in 2 papers)

Affine nonsystematic codes

S. A. Malyugin

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: A perfect binary code $C$ of length $n=2^k-1$ is called affine systematic if there exists a $k$-dimensional subspace of $\{0,1\}^n$ such that the intersection of $C$ and any coset with respect to this subspace is a singleton; otherwise $C$ is called affine nonsystematic. We describe the construction of affine nonsystematic codes. Bibliogr. 12.

Keywords: perfect code, Hamming code, nonsystematic code, affine nonsystematic code, component.

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English version:
Journal of Applied and Industrial Mathematics, 2012, 6:4, 451–459

Bibliographic databases:

UDC: 519.8
Received: 23.10.2011

Citation: S. A. Malyugin, “Affine nonsystematic codes”, Diskretn. Anal. Issled. Oper., 19:4 (2012), 73–85; J. Appl. Industr. Math., 6:4 (2012), 451–459

Citation in format AMSBIB
\Bibitem{Mal12}
\by S.~A.~Malyugin
\paper Affine nonsystematic codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 4
\pages 73--85
\mathnet{http://mi.mathnet.ru/da699}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3013545}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 4
\pages 451--459
\crossref{https://doi.org/10.1134/S1990478912040060}


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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. S. A. Malyugin, “Affine $3$-nonsystematic codes”, J. Appl. Industr. Math., 8:4 (2014), 552–556  mathnet  crossref  mathscinet
    2. 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
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