P. Boyvalenkov, K. Delchev, D. V. Zinoviev, V. A. Zinoviev, “On $q$-ary codes with two distances $d$ and $d+1$”, Probl. Peredachi Inf., 2020, Volume 56, Issue 1,Pages 38

This article is cited in 7 papers

Coding Theory

On $q$-ary codes with two distances $d$ and $d+1$

P. Boyvalenkov^ab, K. Delchev^b, D. V. Zinoviev^c, V. A. Zinoviev^c

^a Technical Faculty, South-Western University, Blagoevgrad, Bulgaria
^b Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
^c Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: We consider $q$-ary block codes with exactly two distances: $d$ and $d + 1$. Several constructions of such codes are given. In the linear case, we show that all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for the maximum cardinality of such codes are derived. Tables of lower and upper bounds for small $q$ and $n$ are presented.

Keywords: two-distance codes, equidistant codes, bounds for codes.

UDC: 621.391.15

Received: 29.05.2019
Revised: 27.10.2019
Accepted: 29.11.2019

DOI: 10.31857/S0555292320010040