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Problemy Peredachi Informatsii, 2020, Volume 56, Issue 4, Pages 10–18
DOI: https://doi.org/10.31857/S0555292320040026 (Mi ppi2325) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Coding Theory

On bases of BCH codes with designed distance $3$ and their extensions

I. Yu. Mogilnykhabc, F. I. Solov'evaab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Regional Scientific and Educational Mathematical Center, Tomsk State University, Tomsk, Russia
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DOI: https://doi.org/10.31857/S0555292320040026
Abstract: We consider narrow-sense BCH codes of length $p^m-1$ over ${{\mathbb{F}}}_{p}$, $m\geqslant3$. We prove that neither such a code with designed distance $\delta=3$ nor its extension for $p\geqslant5$ is generated by the set of its codewords of the minimum nonzero weight. We establish that extended BCH codes with designed distance $\delta=3$ for $p\geqslant3$ are generated by the set of codewords of weight $5$, where basis vectors can be chosen from affine orbits of some codewords.
Keywords: BCH code, cyclic code, affine-invariant code, minimum weight basis, single orbit affine generator.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2020-1479/1
The research was supported in part by the Ministry of Science and Higher Education of the Russian Federation, contract no. 075-02-2020-1479/1.
Received: 10.07.2020
Revised: 26.10.2020
Accepted: 27.10.2020
English version:
Problems of Information Transmission, 2020, Volume 56, Issue 4, Pages 309–316
DOI: https://doi.org/10.1134/S003294602004002X
Bibliographic databases:
Document Type: Article
UDC: 621.391 : 519.725
Language: Russian
Citation: I. Yu. Mogilnykh, F. I. Solov'eva, “On bases of BCH codes with designed distance $3$ and their extensions”, Probl. Peredachi Inf., 56:4 (2020), 10–18; Problems Inform. Transmission, 56:4 (2020), 309–316
Citation in format AMSBIB
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\by I.~Yu.~Mogilnykh, F.~I.~Solov'eva
\paper On bases of BCH codes with designed distance $3$ and their extensions
\jour Probl. Peredachi Inf.
\yr 2020
\vol 56
\issue 4
\pages 10--18
\mathnet{http://mi.mathnet.ru/ppi2325}
\crossref{https://doi.org/10.31857/S0555292320040026}
\transl
\jour Problems Inform. Transmission
\yr 2020
\vol 56
\issue 4
\pages 309--316
\crossref{https://doi.org/10.1134/S003294602004002X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000612377800002}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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