V. K. Leont'ev, G. L. Movsisyan, Zh. G. Margaryan, “Constant weight perfect and <nobr>$D$</nobr>-representable codes”, Proceedings of the YSU, Physical and Mathematical Sciences, 2012, Issue 1,Pages <nobr>16

This article is cited in 3 papers

Mathematics

Constant weight perfect and $D$-representable codes

V. K. Leont'ev^a, G. L. Movsisyan^b, Zh. G. Margaryan^c

^a Computer Centre, Russian Academy of Sciences, Moscow, Russia
^b BIT Group, Moscow, Russia
^c Chair of Discrete Mathematics and Theoretical Informatics YSU, Armenia

Abstract: The problem of the existence of non trivial constant weight perfect codes in the $B^n$-space defined over $GF(2)$ remains unsolved up to now. It has been proved in the present paper that the problem of the existence of constant weight perfect codes is equivalent to the problem of the existence of $D$-representable codes in the fixed layer.

Keywords: constant weight perfect codes, space splitting, Dirichlet regions, $D$-representable codes.

Received: 04.04.2011
Accepted: 30.08.2011

Language: English