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Diskretnyi Analiz i Issledovanie Operatsii, 2012, Volume 19, Issue 2, Pages 84–91 (Mi da684)  
This article is cited in 3 scientific papers (total in 3 papers)

On the admissible families of components of Hamming codes

A. M. Romanov

S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
Full-text PDF (252 kB) Citations (3)
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Abstract: We describe the properties of the $i$-components of Hamming codes. We suggest constructions of the admissible families of components of Hamming codes. It is shown that every $q$-ary code of length $m$ and minimum distance 5 (for $q=3$ the minimum distance is 3) can be embedded in a $q$-ary 1-perfect code of length $n=(q^m-1)/(q-1)$. It is also demonstrated that every binary code of length $m+k$ and minimum distance $3k+3$ can be embedded in a binary 1-perfect code of length $n=2^m-1$. Bibliogr. 5.
Keywords: Hamming code, 1-perfect code, $q$-ary code, binary code, $i$-component.
Received: 13.05.2011
Revised: 21.11.2011
English version:
Journal of Applied and Industrial Mathematics, 2012, Volume 6, Issue 3, Pages 355–359
DOI: https://doi.org/10.1134/S1990478912030106
Bibliographic databases:
Document Type: Article
UDC: 519.176
Language: Russian
Citation: A. M. Romanov, “On the admissible families of components of Hamming codes”, Diskretn. Anal. Issled. Oper., 19:2 (2012), 84–91; J. Appl. Industr. Math., 6:3 (2012), 355–359
Citation in format AMSBIB
\Bibitem{Rom12}
\by A.~M.~Romanov
\paper On the admissible families of components of Hamming codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 2
\pages 84--91
\mathnet{http://mi.mathnet.ru/da684}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2978614}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 3
\pages 355--359
\crossref{https://doi.org/10.1134/S1990478912030106}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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