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Diskretn. Anal. Issled. Oper., 2013, Volume 20, Number 4, Pages 46–64 (Mi da739)  

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

Steiner quadruple systems of small ranks and extended perfect binary codes

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

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

Abstract: Using the switching method, we give a classification of Steiner quadruple systems of order $N>8$ and rank $r_N$ (different by 2 from the rank of the Hamming code of length $N$) which are embedded into extended perfect binary codes of length $N$ and the same rank. Lower and upper bounds for the number of such different systems are provided. The lower bound and description of different Steiner quadruple systems of order $N$ and rank $r_N$ which are not embedded into extended perfect binary codes of length $N$ and the same rank are given. Tab. 4, bibliogr. 22.

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

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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:4, 522–536

Bibliographic databases:

UDC: 621.391.15
Received: 11.10.2012
Revised: 06.06.2013

Citation: D. I. Kovalevskaya, F. I. Solov'eva, “Steiner quadruple systems of small ranks and extended perfect binary codes”, Diskretn. Anal. Issled. Oper., 20:4 (2013), 46–64; J. Appl. Industr. Math., 7:4 (2013), 522–536

Citation in format AMSBIB
\Bibitem{KovSol13}
\by D.~I.~Kovalevskaya, F.~I.~Solov'eva
\paper Steiner quadruple systems of small ranks and extended perfect binary codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2013
\vol 20
\issue 4
\pages 46--64
\mathnet{http://mi.mathnet.ru/da739}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3114912}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 4
\pages 522--536
\crossref{https://doi.org/10.1134/S1990478913040078}


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    Erratum
    • Letter to the Editor
      D. I. Kovalevskaya, F. I. Solov'eva
      Diskretn. Anal. Issled. Oper., 2013, 20:6, 95–96


    This publication is cited in the following articles:
    1. Yu. V. Tarannikov, “O rangakh podmnozhestv prostranstva dvoichnykh vektorov, dopuskayuschikh vstraivanie sistemy Shteinera $S(2,4,v)$”, PDM, 2014, no. 1(23), 73–76  mathnet
  • Дискретный анализ и исследование операций
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