Volume 19, No 4, 2012, P. 73-85

UDC 519.8
S. A. Malyugin
Affine nonsystematic codes

Abstract:
A perfect binary code C of length n = 2^k − 1 is called affine systematic if there exists
a k-dimensional subspace of {0, 1}ⁿ such that the intersection of C and any coset with respect to this subspace is a singleton; otherwise C is called affine nonsystematic. We describe the construction of affine nonsystematic codes.
Bibliogr. 12.

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

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