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Problemy Peredachi Informatsii, 2023, Volume 59, Issue 3, Pages 26–39
DOI: https://doi.org/10.31857/S0555292323030026 (Mi ppi2402) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Coding Theory

On the classification of completely regular codes with covering radius two and antipodal duals

J. Borgesa, V. A. Zinovievb, D. V. Zinovievb

a Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, Barcelona, Spain
b Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.31857/S0555292323030026
Abstract: We classify all linear completely regular codes which have covering radius $\rho=2$ and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights $d$ and $n$.
Keywords: linear completely regular code, code with covering radius $2$, code with an antipodal dual, two-weight code, difference matrix, Latin square, projective oval, equidistant code, Hadamard matrix, Hamming code, maximal arc.
Funding agency Grant number
Science and Education Foundation 20-51-18002
Ministerio de Economía y Competitividad de España PID2022-137924NB-I00 (AEI/FEDER UE)
RED2022-134306-T
Agència de Gestiö d'Ajuts Universitaris i de Recerca 2021-SGR-00643
This work has been partially supported by the Spanish Ministerio de Ciencia e Innovación under Grant PID2022-137924NB-I00 (AEI/FEDER UE) and RED2022-134306-T, and by the Catalan AGAUR Grant 2021-SGR-00643. The research of the second and third authors of the paper was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences within the program of fundamental research on the topic “Mathematical Foundations of the Theory of Error-Correcting Codes” and was also supported by the National Science Foundation of Bulgaria under project no. 20-51-18002.
Received: 14.06.2023
Revised: 27.11.2023
Accepted: 27.11.2023
English version:
Problems of Information Transmission, 2023, Volume 59, Issue 3, Pages 204–216
DOI: https://doi.org/10.1134/S003294602303002X
Bibliographic databases:
Document Type: Article
UDC: 621.391 : 519.725
Language: Russian
Citation: J. Borges, V. A. Zinoviev, D. V. Zinoviev, “On the classification of completely regular codes with covering radius two and antipodal duals”, Probl. Peredachi Inf., 59:3 (2023), 26–39; Problems Inform. Transmission, 59:3 (2023), 204–216
Citation in format AMSBIB
\Bibitem{BorZinZin23}
\by J.~Borges, V.~A.~Zinoviev, D.~V.~Zinoviev
\paper On the classification of completely regular codes with covering radius two and antipodal duals
\jour Probl. Peredachi Inf.
\yr 2023
\vol 59
\issue 3
\pages 26--39
\mathnet{http://mi.mathnet.ru/ppi2402}
\crossref{https://doi.org/10.31857/S0555292323030026}
\edn{https://elibrary.ru/OKKXRQ}
\transl
\jour Problems Inform. Transmission
\yr 2023
\vol 59
\issue 3
\pages 204--216
\crossref{https://doi.org/10.1134/S003294602303002X}
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