This article is cited in 2 papers

Research papers

On partitions into affine nonequivalent perfect $q$-ary codes

A. V. Los'^ab, F. I. Solov'eva<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University

Abstract: It is proved that there exists a partition of the set $F^N_q$ of all $q$-ary vectors of length $N$ into pairwise affine nonequivalent perfect $q$-ary codes of length $N$ with the Hamming distance $3$ for any $N=(q^m-1)/(q-1)$, where $q=p^r,$ $p$ is prime.

Keywords: perfect $q$-ary code, partition into perfect codes, switching, affine nonequivalence of codes.

UDC: 519.72

MSC: 94B25

Received November 4, 2010, published November 18, 2010