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=(qm−1)/(q−1) are constructed for m≥4 and q≥2, and also for n=3 and non prime q. It is shown that, for q≠3,5, 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
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