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

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., 2013, Volume 49, Issue 3, Pages 40–56 (Mi ppi2115)  

This article is cited in 1 scientific paper (total in 1 paper)

Coding Theory

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

V. A. Zinoviev, D. V. Zinoviev

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

Abstract: The structure of all different Steiner triple systems $S(2^m-1,3,2)$ of rank $2^m-m+2$ over $\mathbb F_2$ is described. This induces a natural recurrent method for constructing Steiner triple systems of any rank. In particular, the method gives all different such systems of order $2^m-1$ and rank $\le2^m-m+2$. The number of such different systems of order $2^m-1$ and rank less than or equal to $2^m-m+2$ which are orthogonal to a given code is found. It is shown that all different triple Steiner systems of order $2^m-1$ and rank $\le2^m-m+2$ are derivative and Hamming. Furthermore, all such triples are embedded in quadruple systems of the same rank and in perfect binary nonlinear codes of the same rank.

Full text: PDF file (1376 kB)
References: PDF file   HTML file

English version:
Problems of Information Transmission, 2013, 49:3, 232–248

Bibliographic databases:

UDC: 621.391.1+519.7
Received: 27.09.2012
Revised: 08.04.2013

Citation: V. A. Zinoviev, D. V. Zinoviev, “Structure of Steiner triple systems $S(2^m-1,3,2)$ of rank $2^m-m+2$ over $\mathbb F_2$”, Probl. Peredachi Inf., 49:3 (2013), 40–56; Problems Inform. Transmission, 49:3 (2013), 232–248

Citation in format AMSBIB
\Bibitem{ZinZin13}
\by V.~A.~Zinoviev, D.~V.~Zinoviev
\paper Structure of Steiner triple systems $S(2^m-1,3,2)$ of rank $2^m-m+2$ over~$\mathbb F_2$
\jour Probl. Peredachi Inf.
\yr 2013
\vol 49
\issue 3
\pages 40--56
\mathnet{http://mi.mathnet.ru/ppi2115}
\elib{http://elibrary.ru/item.asp?id=21895672}
\transl
\jour Problems Inform. Transmission
\yr 2013
\vol 49
\issue 3
\pages 232--248
\crossref{https://doi.org/10.1134/S0032946013030034}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000325562200003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84888336526}


Linking options:
  • http://mi.mathnet.ru/eng/ppi2115
  • http://mi.mathnet.ru/eng/ppi/v49/i3/p40

    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. V. A. Zinoviev, D. V. Zinoviev, “Non-full-rank Steiner quadruple systems $S(v,4,3)$”, Problems Inform. Transmission, 50:3 (2014), 270–279  mathnet  crossref  isi
  • Проблемы передачи информации Problems of Information Transmission
    Number of views:
    This page:194
    Full text:37
    References:36
    First page:16

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