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Diskretn. Anal. Issled. Oper., 2015, Volume 22, Number 1, Pages 32–50 (Mi da805)  

Affine $3$-nonsystematic perfect codes of length 15

S. A. Malyugin

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 there exists a $3$-dimensional subspace $L$ in the space $\{0,1\}^n$ such that the intersection of any of its cosets $L+u$ with $C$ is either empty, or a singleton. Otherwise, the code $C$ is called affine $3$-nonsystematic. In the paper, we construct four nonequivalent affine $3$-nonsystematic codes of length 15. Bibliogr. 12.

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

DOI: https://doi.org/10.17377/daio.2015.22.438

Full text: PDF file (336 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2015, 9:2, 251–262

Bibliographic databases:

UDC: 519.8
Received: 26.01.2014
Revised: 24.09.2014

Citation: S. A. Malyugin, “Affine $3$-nonsystematic perfect codes of length 15”, Diskretn. Anal. Issled. Oper., 22:1 (2015), 32–50; J. Appl. Industr. Math., 9:2 (2015), 251–262

Citation in format AMSBIB
\Bibitem{Mal15}
\by S.~A.~Malyugin
\paper Affine $3$-nonsystematic perfect codes of length~15
\jour Diskretn. Anal. Issled. Oper.
\yr 2015
\vol 22
\issue 1
\pages 32--50
\mathnet{http://mi.mathnet.ru/da805}
\crossref{https://doi.org/10.17377/daio.2015.22.438}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3408337}
\elib{http://elibrary.ru/item.asp?id=23133998}
\transl
\jour J. Appl. Industr. Math.
\yr 2015
\vol 9
\issue 2
\pages 251--262
\crossref{https://doi.org/10.1134/S1990478915020106}


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