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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Probl. Peredachi Inf.:
Year:
Volume:
Issue:
Page:
Find






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


Probl. Peredachi Inf., 2012, Volume 48, Issue 2, Pages 21–47 (Mi ppi2073)  

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

Coding Theory

Steiner triple systems $S(2^m-1,3,2)$ of rank $2^m-m+1$ over $\mathbb F_2$

V. A. Zinoviev, D. V. Zinoviev

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: Steiner systems $S(2^m-1,3,2)$ of rank $2^m-m+1$ over the field $\mathbb F_2$ are considered. A new recursive method for constructing Steiner triple systems of an arbitrary rank is proposed. The number of all Steiner systems of rank $2^m-m+1$ is obtained. Moreover, it is shown that all Steiner triple systems $S(2^m-1,3,2)$ of rank $r\le2^m-m+1$ are derived, i.e., can be completed to Steiner quadruple systems $S(2^m,4,3)$. It is also proved that all such Steiner triple systems are Hamming; i.e., any Steiner triple system $S(2^m-1,3,2)$ of rank $r\le2^m-m+1$ over the field $\mathbb F_2$ occurs as the set of words of weight $3$ of a binary nonlinear perfect code of length $2^m-1$.

Full text: PDF file (366 kB)
References: PDF file   HTML file

English version:
Problems of Information Transmission, 2012, 48:2, 102–126

Bibliographic databases:

UDC: 621.391.1+519.7
Received: 19.12.2011
Revised: 11.04.2012

Citation: V. A. Zinoviev, D. V. Zinoviev, “Steiner triple systems $S(2^m-1,3,2)$ of rank $2^m-m+1$ over $\mathbb F_2$”, Probl. Peredachi Inf., 48:2 (2012), 21–47; Problems Inform. Transmission, 48:2 (2012), 102–126

Citation in format AMSBIB
\Bibitem{ZinZin12}
\by V.~A.~Zinoviev, D.~V.~Zinoviev
\paper Steiner triple systems $S(2^m-1,3,2)$ of rank $2^m-m+1$ over~$\mathbb F_2$
\jour Probl. Peredachi Inf.
\yr 2012
\vol 48
\issue 2
\pages 21--47
\mathnet{http://mi.mathnet.ru/ppi2073}
\transl
\jour Problems Inform. Transmission
\yr 2012
\vol 48
\issue 2
\pages 102--126
\crossref{https://doi.org/10.1134/S0032946012020020}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000306338300002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865769050}


Linking options:
  • http://mi.mathnet.ru/eng/ppi2073
  • http://mi.mathnet.ru/eng/ppi/v48/i2/p21

    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
    Erratum

    This publication is cited in the following articles:
    1. D. I. Kovalevskaya, F. I. Solov'eva, E. S. Filimonova, “Steiner triple systems of small rank embedded into perfect binary codes”, J. Appl. Industr. Math., 7:3 (2013), 380–395  mathnet  crossref  mathscinet
    2. V. A. Zinoviev, D. V. Zinoviev, “Structure of Steiner triple systems $S(2^m-1,3,2)$ of rank $2^m-m+2$ over $\mathbb F_2$”, Problems Inform. Transmission, 49:3 (2013), 232–248  mathnet  crossref  isi  elib
    3. M. E. Kovalenko, T. A. Urbanovich, “On the rank of incidence matrices for points and lines of finite affine and projective geometries over a field of four elements”, Problems Inform. Transmission, 50:1 (2014), 79–89  mathnet  crossref  isi
  • Проблемы передачи информации Problems of Information Transmission
    Number of views:
    This page:538
    Full text:98
    References:37
    First page:38

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