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Probl. Peredachi Inf., 2009, Volume 45, Issue 4, Pages 26–42 (Mi ppi1997)  

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

Coding Theory

On one transformation of Steiner quadruple systems $S(v,4,3)$

V. A. Zinoviev, D. V. Zinoviev

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: A transformation of Steiner quadruple systems $S(v,4,3)$ is introduced. For a given system, it allows to construct new systems of the same order, which can be nonisomorphic to the given one. The structure of Steiner systems $S(v,4,3)$ is considered. There are two different types of such systems, namely, induced and singular systems. Induced systems of 2-rank $r$ can be constructed by the introduced transformation of Steiner systems of 2-rank $r-1$ or less. A sufficient condition for a Steiner system $S(v,4,3)$ to be induced is obtained.

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English version:
Problems of Information Transmission, 2009, 45:4, 317–332

Bibliographic databases:

UDC: 621.391.15+519.1
Received: 16.06.2008
Revised: 12.08.2009

Citation: V. A. Zinoviev, D. V. Zinoviev, “On one transformation of Steiner quadruple systems $S(v,4,3)$”, Probl. Peredachi Inf., 45:4 (2009), 26–42; Problems Inform. Transmission, 45:4 (2009), 317–332

Citation in format AMSBIB
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\by V.~A.~Zinoviev, D.~V.~Zinoviev
\paper On one transformation of Steiner quadruple systems $S(v,4,3)$
\jour Probl. Peredachi Inf.
\yr 2009
\vol 45
\issue 4
\pages 26--42
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2641324}
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\jour Problems Inform. Transmission
\yr 2009
\vol 45
\issue 4
\pages 317--332
\crossref{https://doi.org/10.1134/S0032946009040036}
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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. V. A. Zinoviev, D. V. Zinoviev, “Steiner systems $S(v,k,k-1)$: components and rank”, Problems Inform. Transmission, 47:2 (2011), 130–148  mathnet  crossref  mathscinet  isi
    2. Ostergard P.R.J., “Switching codes and designs”, Discrete Math, 312:3 (2012), 621–632  crossref  mathscinet  zmath  isi  elib
    3. Krotov D.S., Mogilnykh I.Yu., Potapov V.N., “To the Theory of Q-Ary Steiner and Other-Type Trades”, Discrete Math., 339:3 (2016), 1150–1157  crossref  mathscinet  zmath  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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