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Problemy Peredachi Informatsii, 2020, Volume 56, Issue 1, Pages 38–50
DOI: https://doi.org/10.31857/S0555292320010040 (Mi ppi2310) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Coding Theory

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

P. Boyvalenkovab, K. Delchevb, D. V. Zinovievc, V. A. Zinovievc

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
Full-text PDF (201 kB) Citations (8)
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DOI: https://doi.org/10.31857/S0555292320010040
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.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00364
Ministry of Education and Science of Bulgaria
The first author was partially supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security” (ICTinSES) of the Bulgarian Ministry of Education and Science. The second author was supported by the National Program “Young Scientists and PostDocs” of the Bulgarian Ministry of Education and Science. The research of the third and forth authors was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Foundation for Basic Research (project no. 19-01-00364).
Received: 29.05.2019
Revised: 27.10.2019
Accepted: 29.11.2019
English version:
Problems of Information Transmission, 2020, Volume 56, Issue 1, Pages 33–44
DOI: https://doi.org/10.1134/S0032946020010044
Bibliographic databases:
Document Type: Article
UDC: 621.391.15
Language: Russian
Citation: P. Boyvalenkov, K. Delchev, D. V. Zinoviev, V. A. Zinoviev, “On $q$-ary codes with two distances $d$ and $d+1$”, Probl. Peredachi Inf., 56:1 (2020), 38–50; Problems Inform. Transmission, 56:1 (2020), 33–44
Citation in format AMSBIB
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\paper On $q$-ary codes with two distances $d$ and $d+1$
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\vol 56
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\pages 38--50
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\jour Problems Inform. Transmission
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Проблемы передачи информации Problems of Information Transmission
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