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Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 5, Pages 47–62 (Mi da704)  

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

Steiner quadruple systems of small rank embedded into extended perfect binary codes

D. I. Kovalevskayaa, F. I. Solov'evaab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: It is known that the set of all vectors of weight 4 in an arbitrary extended perfect binary code of length $N$ containing the all-zero vector defines a Steiner quadruple system of order $N$. In this paper, we give a modification of the known Lindner construction for the Steiner quadruple system of order $N=2^r$ that can be represented by some special switchings from the Hamming system of Steiner quadruples. It is proved that any of such Steiner quadruple systems is embedded into some extended perfect binary code constructed by switchings of $ijkl$-components from the binary extended Hamming code. We present the lower bound for the number of different Steiner quadruple systems of order $N$ of rank less than or equal to $N-\log N+1$ such that the systems are embedded into extended perfect binary codes of length $N$. Tab. 4, bibliogr. 19.

Keywords: Steiner quadruple system, extended perfect binary code, switching, $ijkl$-component, $il$-component.

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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:1, 68–77

Bibliographic databases:

UDC: 621.391.15
Received: 14.10.2011
Revised: 10.02.2012

Citation: D. I. Kovalevskaya, F. I. Solov'eva, “Steiner quadruple systems of small rank embedded into extended perfect binary codes”, Diskretn. Anal. Issled. Oper., 19:5 (2012), 47–62; J. Appl. Industr. Math., 7:1 (2013), 68–77

Citation in format AMSBIB
\Bibitem{KovSol12}
\by D.~I.~Kovalevskaya, F.~I.~Solov'eva
\paper Steiner quadruple systems of small rank embedded into extended perfect binary codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 5
\pages 47--62
\mathnet{http://mi.mathnet.ru/da704}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3058508}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 1
\pages 68--77
\crossref{https://doi.org/10.1134/S1990478913010079}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874509055}


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    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. 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. Yang Zh.-F., Chiou Sh.-Sh., Lee J.-T., “Watermark Design Based on Steiner Triple Systems”, Multimed. Tools Appl., 72:3 (2014), 2177–2194  crossref  isi  elib  scopus
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