Volume 16, No 1, 2009, P. 44-63
S. A. Malyugin
On nonsystematic perfect codes over finite fields
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 $H_q^n$.
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