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Diskretn. Anal. Issled. Oper., 2008, Volume 15, Number 3, Pages 11–21 (Mi da530)  

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

On mobile sets in the binary hypercube

Yu. L. Vasil'ev, S. V. Avgustinovich, D. S. Krotov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: If two distance-3 codes have the same neighborhood, then each of them is called a mobile set. In the $(4k+3)$-dimensional binary hypercube there exists a mobile set of cardinality $2\cdot6^k$ that cannot be split into mobile sets of smaller cardinalities or represented as a natural extension of a mobile set of smaller dimension. Bibl. 10.

Keywords: 1-perfect code, Bollean cube, mobile set, $i$-component.

Full text: PDF file (273 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2009, 3:2, 290–296

Bibliographic databases:

UDC: 519.72
Received: 27.12.2007
Revised: 03.04.2008

Citation: Yu. L. Vasil'ev, S. V. Avgustinovich, D. S. Krotov, “On mobile sets in the binary hypercube”, Diskretn. Anal. Issled. Oper., 15:3 (2008), 11–21; J. Appl. Industr. Math., 3:2 (2009), 290–296

Citation in format AMSBIB
\Bibitem{VasAvgKro08}
\by Yu.~L.~Vasil'ev, S.~V.~Avgustinovich, D.~S.~Krotov
\paper On mobile sets in the binary hypercube
\jour Diskretn. Anal. Issled. Oper.
\yr 2008
\vol 15
\issue 3
\pages 11--21
\mathnet{http://mi.mathnet.ru/da530}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2542321}
\zmath{https://zbmath.org/?q=an:1249.94059}
\transl
\jour J. Appl. Industr. Math.
\yr 2009
\vol 3
\issue 2
\pages 290--296
\crossref{https://doi.org/10.1134/S199047890902015X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-66149129563}


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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. Avgustinovich S.V., Krotov D.S., “Embedding in a Perfect Code”, J Combin Des, 17:5 (2009), 419–423  crossref  mathscinet  zmath  isi  scopus
    2. 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
    3. V. N. Potapov, “Cardinality spectra of components of correlation immune functions, bent functions, perfect colorings, and codes”, Problems Inform. Transmission, 48:1 (2012), 47–55  mathnet  crossref  isi
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