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JOURNALS // Diskretnyi Analiz i Issledovanie Operatsii // Archive

Diskretn. Anal. Issled. Oper., 2012 Volume 19, Issue 4, Pages 73–85 (Mi da699)

This article is cited in 2 papers

Affine nonsystematic codes

S. A. Malyugin

Sobolev Institute of Mathematics, Novosibirsk, Russia

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.

UDC: 519.8

Received: 23.10.2011


 English version:
Journal of Applied and Industrial Mathematics, 2012, 6:4, 451–459

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