Volume 22, No 1, 2015, P. 32-50
UDC 519.8
S. A. Malyugin
Affine 3-nonsystematic perfect codes of length 15
Abstract:
A perfect binary code C of length n = 2k − 1 is called affine 3-systematic if there exists a 3-dimensional subspace L in the space {0, 1}n such that the intersection of any of its cosetsL + u with C is either empty, or a singleton. Otherwise, the code C is called affine 3-nonsystematic. In the paper, we construct four nonequivalent affine 3-nonsystematic codes of length 15.
Bibliogr. 12.
Keywords: perfect code, Hamming code, nonsystematic code, affine nonsystematic code, affine 3-nonsystematic code, component.
DOI: 10.17377/daio.2015.22.438
Sergey A. Malyugin1
1. Sobolev Institute of Mathematics
4 Koptyug Ave., 630090 Novosibirsk, Russia
å-mail: mal@math.nsc.ru
Received 26 January 2014
Revised 24 September 2014
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