RUS  ENG
Full version
JOURNALS // Diskretnyi Analiz i Issledovanie Operatsii // Archive

Diskretn. Anal. Issled. Oper., 2009 Volume 16, Issue 1, Pages 44–63 (Mi da561)

This article is cited 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.

UDC: 519.72

Received: 31.07.2008


 English version:
Journal of Applied and Industrial Mathematics, 2010, 4:2, 218–230

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024