P. Boyvalenkov, D. Danev, M. Stoyanova, “Refinements of Levenshtein bounds in <nobr>$q$</nobr>-ary Hamming spaces”, Probl. Peredachi Inf., 2018, Volume 54, Issue 4,Pages <nobr>35

This article is cited in 1 paper

Coding Theory

Refinements of Levenshtein bounds in $q$-ary Hamming spaces

P. Boyvalenkov^ab, D. Danev^c, M. Stoyanova^d

^a Faculty of Engineering, South-Western University, Blagoevgrad, Bulgaria
^b Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
^c Department of Electrical Engineering and Department of Mathematics, Linköping University, Linköping, Sweden
^d Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria

Abstract: We develop refinements of the Levenshtein bound in $q$-ary Hamming spaces by taking into account the discrete nature of the distances versus the continuous behavior of certain parameters used by Levenshtein. We investigate the first relevant cases and present new bounds. In particular, we derive generalizations and $q$-ary analogs of the MacEliece bound. Furthermore, we provide evidence that our approach is as good as the complete linear programming and discuss how faster are our calculations. Finally, we present a table with parameters of codes which, if exist, would attain our bounds.

UDC: 621.391.15

Received: 17.12.2017
Revised: 16.05.2018
Accepted: 10.08.2018