RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Diskr. Mat., 2004, Volume 16, Issue 1, Pages 146–156 (Mi dm149)  

This article is cited in 7 scientific papers (total in 7 papers)

Group codes and their nonassociative generalizations

S. González, E. Couselo, V. T. Markov, A. A. Nechaev


Abstract: We give a complete description (with the use of computation) of the best parameters of linear codes that correspond to the left ideals in the loop algebras $\mathbf F_qL$ for $q\in\{2,3,4,5\}$ and $|L|\le 7$, and also in the group algebras $\mathbf F_qG$ for groups $G$ of order $|G|\le12$. We distinguish the linearly optimal codes, the codes satisfying the Varshamov–Hilbert condition as well as those for which the Plotkin bound is attained. The results suggest that the research in codes constructed by using non-associative and non-semisimple non-commutative algebras can open new possibilities and deserves to be developed.
This research was supported by Russian Foundation for Basic Research, grants 02–01–00218, 02–01–00687, and by grants 1910.2003.1 and 2358.2003.9 of President of Russian Federation for supporting the leading scientific schools.
The last two authors thank University of Oviedo for the hospitality.

DOI: https://doi.org/10.4213/dm149

Full text: PDF file (938 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2004, 14:2, 163–172

Bibliographic databases:

UDC: 519.7
Received: 10.11.2003

Citation: S. González, E. Couselo, V. T. Markov, A. A. Nechaev, “Group codes and their nonassociative generalizations”, Diskr. Mat., 16:1 (2004), 146–156; Discrete Math. Appl., 14:2 (2004), 163–172

Citation in format AMSBIB
\Bibitem{GonCouMar04}
\by S.~Gonz\'alez, E.~Couselo, V.~T.~Markov, A.~A.~Nechaev
\paper Group codes and their nonassociative generalizations
\jour Diskr. Mat.
\yr 2004
\vol 16
\issue 1
\pages 146--156
\mathnet{http://mi.mathnet.ru/dm149}
\crossref{https://doi.org/10.4213/dm149}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2069996}
\zmath{https://zbmath.org/?q=an:1060.94046}
\transl
\jour Discrete Math. Appl.
\yr 2004
\vol 14
\issue 2
\pages 163--172
\crossref{https://doi.org/10.1515/156939204872347}


Linking options:
  • http://mi.mathnet.ru/eng/dm149
  • https://doi.org/10.4213/dm149
  • http://mi.mathnet.ru/eng/dm/v16/i1/p146

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gonzalez S., Martinez C., Nicolas A.P., “Classic and Quantum Error Correcting Codes”, Coding Theory and Applications, Proceedings, Lecture Notes in Computer Science, 5228, 2008, 56–68  crossref  zmath  isi  scopus
    2. Couselo E., Gonzalez S., Markov V., Martinez C., Nechaev A., “Some constructions of linearly optimal group codes”, Linear Algebra and Its Applications, 433:2 (2010), 356–364  crossref  mathscinet  zmath  isi  scopus
    3. C. García Pillado, S. González, V. T. Markov, C. Martínez, A. A. Nechaev, “When are all group codes of a noncommutative group Abelian (a computational approach)?”, J. Math. Sci., 186:4 (2012), 578–585  mathnet  crossref
    4. V. T. Markov, A. V. Mikhalev, A. V. Gribov, P. A. Zolotykh, S. S. Skazhenik, “Kvazigruppy i koltsa v kodirovanii i postroenii kriptoskhem”, PDM, 2012, no. 4(18), 31–52  mathnet
    5. C. García Pillado, S. González, V. T. Markov, C. Martínez, “Non-Abelian group codes over an arbitrary finite field”, J. Math. Sci., 223:5 (2017), 504–507  mathnet  crossref  mathscinet  elib
    6. Garcia Pillado C., Gonzalez S., Markov V., Martinez C., Nechaev A., “New examples of non-abelian group codes”, Adv. Math. Commun., 10:1, SI (2016), 1–10  crossref  mathscinet  isi  scopus
    7. V. T. Markov, A. V. Mikhalev, A. A. Nechaev, “Neassotsiativnye algebraicheskie struktury v kriptografii i kodirovanii”, Fundament. i prikl. matem., 21:4 (2016), 99–124  mathnet  mathscinet
  • Дискретная математика
    Number of views:
    This page:705
    Full text:261
    References:63
    First page:5

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020