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Probl. Peredachi Inf., 2007, Volume 43, Issue 1, Pages 39–55 (Mi ppi5)  

This article is cited in 6 scientific papers (total in 6 papers)

Coding Theory

On Resolvability of Steiner Systems $S(v=2^m,4,3)$ of Rank $r\le v-m+1$ over $\mathbb F_2$

V. A. Zinov'ev, D. V. Zinov'ev

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

Abstract: Two new constructions of Steiner quadruple systems $S(v,4,3)$ are given. Both preserve resolvability of the original Steiner system and make it possible to control the rank of the resulting system. It is proved that any Steiner system $S(v=2^m,4,3)$ of rank $r\le v-m+1$ over $\mathbb F_2$ is resolvable and that all systems of this rank can be constructed in this way. Thus, we find the number of all different Steiner systems of rank $r=v-m+1$.

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English version:
Problems of Information Transmission, 2007, 43:1, 33–47

Bibliographic databases:

UDC: 621.391.1:519.2
Received: 14.02.2006
Revised: 12.09.2006

Citation: V. A. Zinov'ev, D. V. Zinov'ev, “On Resolvability of Steiner Systems $S(v=2^m,4,3)$ of Rank $r\le v-m+1$ over $\mathbb F_2$”, Probl. Peredachi Inf., 43:1 (2007), 39–55; Problems Inform. Transmission, 43:1 (2007), 33–47

Citation in format AMSBIB
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\paper On Resolvability of Steiner Systems $S(v=2^m,4,3)$
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\jour Probl. Peredachi Inf.
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\vol 43
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\pages 39--55
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\jour Problems Inform. Transmission
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Zinoviev, D. V. Zinoviev, “On one transformation of Steiner quadruple systems $S(v,4,3)$”, Problems Inform. Transmission, 45:4 (2009), 317–332  mathnet  crossref  mathscinet  isi
    2. V. A. Zinoviev, D. V. Zinoviev, “Steiner triple systems $S(2^m-1,3,2)$ of rank $2^m-m+1$ over $\mathbb F_2$”, Problems Inform. Transmission, 48:2 (2012), 102–126  mathnet  crossref  isi
    3. D. I. Kovalevskaya, F. I. Solov'eva, “Steiner quadruple systems of small rank embedded into extended perfect binary codes”, J. Appl. Industr. Math., 7:1 (2013), 68–77  mathnet  crossref  mathscinet
    4. 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
    5. 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
    6. V. A. Zinoviev, D. V. Zinoviev, “Generalized Preparata codes and $2$-resolvable Steiner quadruple systems”, Problems Inform. Transmission, 52:2 (2016), 114–133  mathnet  crossref  mathscinet  isi  elib  elib
  • Проблемы передачи информации Problems of Information Transmission
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