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Diskretnyi Analiz i Issledovanie Operatsii, 2009, Volume 16, Issue 1, Pages 44–63
(Mi da561)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/da561 https://www.mathnet.ru/eng/da/v16/i1/p44
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Abstract page: | 299 | Full-text PDF : | 79 | References: | 43 | First page: | 9 |
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