Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find




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

Matematicheskie Zametki, 2020, Volume 107, Issue 2, Pages 178–194
DOI: https://doi.org/10.4213/mzm12194 (Mi mzm12194) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Relationship between Codes and Idempotents in a Dihedral Group Algebra

K. V. Vedeneva, V. M. Deundyakba

a Southern Federal University, Rostov-on-Don
b State Scientific Organization: Research Institute "Spetsvuzavtomatika", Rostov-on-Don
Full-text PDF (544 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm12194
Abstract: Codes in the dihedral group algebra $\mathbb{F}_qD_{2n}$, i.e., left ideals in this algebra, are studied. A generating idempotent is constructed for every code in $\mathbb{F}_qD_{2n}$ given by its image under the Wedderburn decomposition of this algebra. By using a selected set of idempotents, the inverse Wedderburn transform for the algebra $\mathbb{F}_qD_{2n}$ is constructed. The image of some codes under the Wedderburn decomposition is described directly in terms of their generating idempotents. Examples of the application of the obtained results to induced codes are considered.
Keywords: dihedral group, group algebras, idempotents, Wedderburn decomposition, noncommutative codes.
Received: 17.09.2018
English version:
Mathematical Notes, 2020, Volume 107, Issue 2, Pages 201–216
DOI: https://doi.org/10.1134/S0001434620010204
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: Russian
Citation: K. V. Vedenev, V. M. Deundyak, “Relationship between Codes and Idempotents in a Dihedral Group Algebra”, Mat. Zametki, 107:2 (2020), 178–194; Math. Notes, 107:2 (2020), 201–216
Citation in format AMSBIB
\Bibitem{VedDeu20}
\by K.~V.~Vedenev, V.~M.~Deundyak
\paper Relationship between Codes and Idempotents in a Dihedral Group Algebra
\jour Mat. Zametki
\yr 2020
\vol 107
\issue 2
\pages 178--194
\mathnet{http://mi.mathnet.ru/mzm12194}
\crossref{https://doi.org/10.4213/mzm12194}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4070004}
\elib{https://elibrary.ru/item.asp?id=43268870}
\transl
\jour Math. Notes
\yr 2020
\vol 107
\issue 2
\pages 201--216
\crossref{https://doi.org/10.1134/S0001434620010204}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000519555100020}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85080981969}
Linking options:
  • https://www.mathnet.ru/eng/mzm12194
  • https://doi.org/10.4213/mzm12194
  • https://www.mathnet.ru/eng/mzm/v107/i2/p178
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024