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., 2013, Volume 20, Number 3, Pages 3–25 (Mi da729)  

This article is cited in 2 scientific papers (total in 2 papers)

Steiner triple systems of small rank embedded into perfect binary codes

D. I. Kovalevskayaa, F. I. Solov'evaab, E. S. Filimonovaa

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

Abstract: Using the switching method, we classify Steiner triple systems $\mathrm{STS}(n)$ of order $n=2^r-1$, $r>3$, and of small rank $r_n$ (which differs by 2 from the rank of the Hamming code of length $n$) embedded into perfect binary codes of length $n$ and of the same rank. The lower and upper bounds for the number of such different $\mathrm{STS}$ are given. We present the description and the lower bound for the number of $\mathrm{STS}(n)$ of rank $r_n$ which are not embedded into perfect binary codes of length $n$ and of the same rank. The embeddability of any $\mathrm{STS}(n)$ of rank $r_n-1$ into a perfect code of length $n$ with the same rank, given by VasilТev construction, is proved. Bibliogr. 22.

Keywords: Steiner triple system, perfect binary code, switching, Pasch configuration, $ijk$-component, $i$-component.

Full text: PDF file (338 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2013, 7:3, 380–395

Bibliographic databases:

UDC: 621.391.15
Received: 02.08.2012
Revised: 20.03.2013

Citation: D. I. Kovalevskaya, F. I. Solov'eva, E. S. Filimonova, “Steiner triple systems of small rank embedded into perfect binary codes”, Diskretn. Anal. Issled. Oper., 20:3 (2013), 3–25; J. Appl. Industr. Math., 7:3 (2013), 380–395

Citation in format AMSBIB
\Bibitem{KovSolFil13}
\by D.~I.~Kovalevskaya, F.~I.~Solov'eva, E.~S.~Filimonova
\paper Steiner triple systems of small rank embedded into perfect binary codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 3
\pages 3--25
\mathnet{http://mi.mathnet.ru/da729}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3135741}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 3
\pages 380--395
\crossref{https://doi.org/10.1134/S1990478913030113}


Linking options:
  • http://mi.mathnet.ru/eng/da729
  • http://mi.mathnet.ru/eng/da/v20/i3/p3

    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. D. I. Kovalevskaya, F. I. Solov'eva, “Steiner quadruple systems of small ranks and extended perfect binary codes”, J. Appl. Industr. Math., 7:4 (2013), 522–536  mathnet  crossref  mathscinet
    2. M. V. Vedunova, A. O. Ignatova, K. L. Geut, “Blokirovka lineinykh mnogoobrazii i troiki Shteinera”, PDM. Prilozhenie, 2019, no. 12, 93–95  mathnet  crossref
  • ƒискретный анализ и исследование операций
    Number of views:
    This page:188
    Full text:62
    References:29
    First page:2

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