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Diskretnyi Analiz i Issledovanie Operatsii, 2009, Volume 16, Issue 1, Pages 44–63 (Mi da561)  

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

On nonsystematic perfect codes over finite fields

S. A. Malyugin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (308 kB) Citations (2)
References:
Abstract: Nonsystematic perfect $q$-ary codes over a field $F_q$ of length $n=(q^m-1)/(q-1)$ are constructed for $m\ge4$ and $q\ge2$, and also for $n=3$ and non prime $q$. It is shown that, for $q\ne3,5$, such codes can be constructed by switchings seven disjoint components and, for $q=3,5$, by switchings eight disjoint components of the Hamming code $H_q^n$. Bibl. 12.
Keywords: perfect code, Hamming code, Galois field, nonsystematic code, projective geometry, component.
Received: 31.07.2008
English version:
Journal of Applied and Industrial Mathematics, 2010, Volume 4, Issue 2, Pages 218–230
DOI: https://doi.org/10.1134/S1990478910020110
Bibliographic databases:
UDC: 519.72
Language: Russian
Citation: S. A. Malyugin, “On nonsystematic perfect codes over finite fields”, Diskretn. Anal. Issled. Oper., 16:1 (2009), 44–63; J. Appl. Industr. Math., 4:2 (2010), 218–230
Citation in format AMSBIB
\Bibitem{Mal09}
\by S.~A.~Malyugin
\paper On nonsystematic perfect codes over finite fields
\jour Diskretn. Anal. Issled. Oper.
\yr 2009
\vol 16
\issue 1
\pages 44--63
\mathnet{http://mi.mathnet.ru/da561}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2543162}
\zmath{https://zbmath.org/?q=an:1249.94066}
\transl
\jour J. Appl. Industr. Math.
\yr 2010
\vol 4
\issue 2
\pages 218--230
\crossref{https://doi.org/10.1134/S1990478910020110}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77953489263}
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  • https://www.mathnet.ru/eng/da/v16/i1/p44
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретный анализ и исследование операций
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    Abstract page:299
    Full-text PDF :79
    References:43
    First page:9
     
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