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Problemy Peredachi Informatsii, 2022, Volume 58, Issue 3, Pages 33–44
DOI: https://doi.org/10.31857/S0555292322030032 (Mi ppi2373) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Coding Theory

On weight distributions for a class of codes with parameters of Reed–Muller codes

I. Yu. Mogilnykha, F. I. Solov'eva

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
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DOI: https://doi.org/10.31857/S0555292322030032
Abstract: We present a new construction method for a doubly exponential class of binary codes with the parameters of Reed–Muller codes. We investigate the weight spectrum and the distance-invariance property of the proposed codes. In the constructed class of codes with the parameters of Reed–Muller codes, we show the existence of codes with the same weight distribution as for a Reed–Muller code and of codes with weight distributions other than this. We establish that all codes with the parameters of the Reed–Muller code which are obtained by the Vasil’ev–Pulatov construction but are distinct from extended perfect codes either are equivalent to the original Reed–Muller codes or have distance distributions different from those.
Keywords: Reed–Muller code, code with the parameters of a Reed–Muller code, weight distribution, distance invariance, generalized Pulatov construction, switching construction.
Funding agency Grant number
Russian Science Foundation 22-21-00135
The research was carried out at the expense of the Russian Science Foundation, project no. 22 21-00135, https://rscf.ru/en/project/22-21-00135/.
Received: 01.04.2022
Revised: 16.06.2022
Accepted: 18.06.2022
English version:
Problems of Information Transmission, 2022, Volume 58, Issue 3, Pages 231–241
DOI: https://doi.org/10.1134/S0032946022030036
Bibliographic databases:
Document Type: Article
UDC: 621.391.1 : 519.725
Language: Russian
Citation: I. Yu. Mogilnykh, F. I. Solov'eva, “On weight distributions for a class of codes with parameters of Reed–Muller codes”, Probl. Peredachi Inf., 58:3 (2022), 33–44; Problems Inform. Transmission, 58:3 (2022), 231–241
Citation in format AMSBIB
\Bibitem{MogSol22}
\by I.~Yu.~Mogilnykh, F.~I.~Solov'eva
\paper On weight distributions for a class of codes with parameters of Reed--Muller codes
\jour Probl. Peredachi Inf.
\yr 2022
\vol 58
\issue 3
\pages 33--44
\mathnet{http://mi.mathnet.ru/ppi2373}
\edn{https://elibrary.ru/EAAOCA}
\transl
\jour Problems Inform. Transmission
\yr 2022
\vol 58
\issue 3
\pages 231--241
\crossref{https://doi.org/10.1134/S0032946022030036}
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