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JOURNALS // Diskretnyi Analiz i Issledovanie Operatsii // Archive
Diskretn. Anal. Issled. Oper., 2016 Volume 23, Issue 4, Pages 26–34 (Mi da857)
On the embedding of constant-weight codes into perfect codes

A. M. Romanov

Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: We show that each $q$-ary constant-weight code of weight 3, minimum distance 4, and length $m$ can be embedded in a $q$-ary $1$-perfect code of length $n=(q^m-1)/(q-1)$. Bibliogr. 10.

Keywords: Hamming code, nonlinear perfect code, constant-weight code, $i$-component.

UDC: 519.7

Received: 22.03.2016
Revised: 26.04.2016

DOI: 10.17377/daio.2016.23.533


 English version: Journal of Applied and Industrial Mathematics, 2016, 10:4, 556–559

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© Steklov Math. Inst. of RAS, 2024