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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 2, Pages 1358–1366
DOI: https://doi.org/10.33048/semi.2021.18.103 (Mi semr1444) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Discrete mathematics and mathematical cybernetics

Minimum weight bases for quaternary Reed – Muller codes

F. I. Solov'eva

Sobolev Institute of Mathematics, 4, Acad. Koptyuga ave., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.103
Abstract: The quaternary Plotkin and BQ-Plotkin constructions giving the families of quaternary Reed – Muller codes were presented in 2009. The Gray map image of the obtained $\mathbb{Z}_4$-linear codes have the same parameters and fundamental properties as the codes in the classical binary linear Reed – Muller family. We have found one more general property for the families of quaternary Reed – Muller codes that is common with binary Reed – Muller codes: all these quaternary codes have bases of minimum weight codewords. The bases are constructed by induction.
Keywords: Reed – Muller code, quaternary code, additive code, quaternary Reed – Muller code, minimum weight basis, $\mathbb{Z}_4$-linear code.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00682
The work is supported by RFBR (grant 19-01-00682).
Received December 12, 2020, published November 24, 2021
Bibliographic databases:
Document Type: Article
UDC: 519.725
MSC: 94B60
Language: English
Citation: F. I. Solov'eva, “Minimum weight bases for quaternary Reed – Muller codes”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 1358–1366
Citation in format AMSBIB
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\by F.~I.~Solov'eva
\paper Minimum weight bases for quaternary Reed -- Muller codes
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 2
\pages 1358--1366
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\crossref{https://doi.org/10.33048/semi.2021.18.103}
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