Volume 21, No 4, 2014, P. 54-61

UDC 519.8
S. A. Malyugin
Affine 3-nonsystematic codes

Abstract:
A perfect binary code C of length n = 2^k − 1 is called affine 3-nonsystematic if in the space {0, 1}ⁿ there exists a 3-dimensional subspace L such that the intersection of any of its cosets L+u with the code C is either empty or a singleton. Otherwise, the code C is called affine 3-nonsystematic. We construct affine 3-nonsystematic codes of length n = 2^k − 1,
k > 4. 
Bibliogr. 11.

Keywords: perfect code, Hamming code, nonsystematic code, affine nonsystematic code, affine 3-nonsystematic code, component.

Malyugin Serguey Artemievich ^1,2
1. S. L. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: mal@math.nsc.ru