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Volume 16, No 1, 2009, P. 44-63

UDC 519.72
S. A. Malyugin
On nonsystematic perfect codes over finite fields

Abstract:
Nonsystematic perfect q-ary codes over a field Fq of length n=(qm1)/(q1) are constructed for m4 and q2, and also for n=3 and non prime q. It is shown that, for q3,5, such codes can be constructed by switchings seven disjoint components and, for q=3,5, by switchings eight disjoint components of the Hamming code Hnq.
Bibl. 12.

Keywords: perfect code, Hamming code, Galois field, nonsystematic code, projective geometry, component.

Malyugin Sergey Artem’evich 1
1. S. L. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: malugin@math.nsc.ru

 © Sobolev Institute of Mathematics, 2015