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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1689–1702
DOI: https://doi.org/10.33048/semi.2019.16.119 (Mi semr1160) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Discrete mathematics and mathematical cybernetics

A concatenation construction for propelinear perfect codes from regular subgroups of $\mathrm{GA}(r,2)$

I. Yu. Mogilnykhab, F. I. Solov'evaa

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Tomsk State University, Regional Scientific and Educational Mathematical Center, 36, Lenina ave., Tomsk, 634050, Russia
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DOI: https://doi.org/10.33048/semi.2019.16.119
Abstract: A code $C$ is called propelinear if there is a subgroup of $\mathrm{Aut}(C)$ of order $|C|$ acting transitively on the codewords of $C$. In the paper new propelinear perfect binary codes of any admissible length more than $7$ are obtained by a particular case of the Solov'eva concatenation construction–1981 and the regular subgroups of the general affine group of the vector space over $\mathrm{GF}(2)$.
Keywords: Hamming code, perfect code, concatenation construction, propelinear code, Mollard code, regular subgroup, transitive action.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.13557.2019/13.1
The work was supported by the Ministry of Education and Science of Russia (state assignment No. 1.13557.2019/13.1).
Received March 15, 2019, published November 21, 2019
Bibliographic databases:
Document Type: Article
UDC: 519.725
MSC: 94B60
Language: English
Citation: I. Yu. Mogilnykh, F. I. Solov'eva, “A concatenation construction for propelinear perfect codes from regular subgroups of $\mathrm{GA}(r,2)$”, Sib. Èlektron. Mat. Izv., 16 (2019), 1689–1702
Citation in format AMSBIB
\Bibitem{MogSol19}
\by I.~Yu.~Mogilnykh, F.~I.~Solov'eva
\paper A concatenation construction for propelinear perfect codes from regular subgroups of $\mathrm{GA}(r,2)$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1689--1702
\mathnet{http://mi.mathnet.ru/semr1160}
\crossref{https://doi.org/10.33048/semi.2019.16.119}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000497717700003}
Linking options:
  • https://www.mathnet.ru/eng/semr1160
  • https://www.mathnet.ru/eng/semr/v16/p1689
    • This publication is cited in the following articles:
    1. I. Yu. Mogilnykh, F. I. Solov'eva, “Coordinate transitivity of a class of extended perfect codes and their SQS”, Sib. elektron. matem. izv., 17 (2020), 1451–1462  mathnet  crossref
    2. I. Yu. Mogilnykh, “On $q$-ary propelinear perfect codes based on regular subgroups of the general affine group”, Problems Inform. Transmission, 58:1 (2022), 58–71  mathnet  crossref  crossref  isi
    3. I. Yu. Mogilnykh, F. I. Soloveva, “Konstruktsii i invarianty optimalnykh kodov v metrike Li”, Probl. peredachi inform., 59:2 (2023), 3–17  mathnet  crossref
    4. I. Yu. Mogilnykh, F. I. Solov'eva, “Constructions and Invariants of Optimal Codes in the Lee Metric”, Probl Inf Transm, 59:2 (2023), 71  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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