Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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 3 scientific papers (total in 3 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
Full-text PDF (418 kB) Citations (3)
References:
PDF
HTML
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
\Bibitem{Sol21}
\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
\mathnet{http://mi.mathnet.ru/semr1444}
\crossref{https://doi.org/10.33048/semi.2021.18.103}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000734395000023}
Linking options:
  • https://www.mathnet.ru/eng/semr1444
  • https://www.mathnet.ru/eng/semr/v18/i2/p1358
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:88
    Full-text PDF :38
    References:28
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024