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



Diskretn. Anal. Issled. Oper.:
Year:
Volume:
Issue:
Page:
Find






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


Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 2, Pages 84–91 (Mi da684)  

This article is cited in 3 scientific papers (total in 3 papers)

On the admissible families of components of Hamming codes

A. M. Romanov

S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

Abstract: We describe the properties of the $i$-components of Hamming codes. We suggest constructions of the admissible families of components of Hamming codes. It is shown that every $q$-ary code of length $m$ and minimum distance 5 (for $q=3$ the minimum distance is 3) can be embedded in a $q$-ary 1-perfect code of length $n=(q^m-1)/(q-1)$. It is also demonstrated that every binary code of length $m+k$ and minimum distance $3k+3$ can be embedded in a binary 1-perfect code of length $n=2^m-1$. Bibliogr. 5.

Keywords: Hamming code, 1-perfect code, $q$-ary code, binary code, $i$-component.

Full text: PDF file (252 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2012, 6:3, 355–359

Bibliographic databases:

UDC: 519.176
Received: 13.05.2011
Revised: 21.11.2011

Citation: A. M. Romanov, “On the admissible families of components of Hamming codes”, Diskretn. Anal. Issled. Oper., 19:2 (2012), 84–91; J. Appl. Industr. Math., 6:3 (2012), 355–359

Citation in format AMSBIB
\Bibitem{Rom12}
\by A.~M.~Romanov
\paper On the admissible families of components of Hamming codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 2
\pages 84--91
\mathnet{http://mi.mathnet.ru/da684}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978614}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 3
\pages 355--359
\crossref{https://doi.org/10.1134/S1990478912030106}


Linking options:
  • http://mi.mathnet.ru/eng/da684
  • http://mi.mathnet.ru/eng/da/v19/i2/p84

    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. Krotov D.S., Sotnikova E.V., “Embedding in Q-Ary 1-Perfect Codes and Partitions”, Discrete Math., 338:11 (2015), 1856–1859  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. M. Romanov, “On full-rank perfect codes over finite fields”, J. Appl. Industr. Math., 10:3 (2016), 444–452  mathnet  crossref  crossref  mathscinet  elib
    3. A. M. Romanov, “On the embedding of constant-weight codes into perfect codes”, J. Appl. Industr. Math., 10:4 (2016), 556–559  mathnet  crossref  crossref  mathscinet  elib
  • ƒискретный анализ и исследование операций
    Number of views:
    This page:340
    Full text:65
    References:25
    First page:4

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