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Diskretn. Anal. Issled. Oper., 2016, Volume 23, Issue 3, Pages 93–106 (Mi da854)  

This article is cited in 7 scientific papers (total in 7 papers)

Metric complements to subspaces in the Boolean cube

A. K. Oblaukhov

Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

Abstract: We study the metric complements to sets in the Boolean cube; i.e. the subsets maximally distant from given subset. We obtain the general form for the metric complement of a linear subspace and some more exact description for the class of subspaces with basis of a special form. It is proved that the completely regular codes (including perfect and uniformly packed) are metrically regular. Bibliogr. 9.

Keywords: subspace, metrically regular set, metric complement, completely regular code, bent-function.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-31-20635


DOI: https://doi.org/10.17377/daio.2016.23.513

Full text: PDF file (280 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2016, 10:3, 397–403

Bibliographic databases:

UDC: 519.7
Received: 22.09.2015
Revised: 09.03.2016

Citation: A. K. Oblaukhov, “Metric complements to subspaces in the Boolean cube”, Diskretn. Anal. Issled. Oper., 23:3 (2016), 93–106; J. Appl. Industr. Math., 10:3 (2016), 397–403

Citation in format AMSBIB
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\by A.~K.~Oblaukhov
\paper Metric complements to subspaces in the Boolean cube
\jour Diskretn. Anal. Issled. Oper.
\yr 2016
\vol 23
\issue 3
\pages 93--106
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\crossref{https://doi.org/10.17377/daio.2016.23.513}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3563718}
\elib{https://elibrary.ru/item.asp?id=26681832}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 3
\pages 397--403
\crossref{https://doi.org/10.1134/S1990478916030108}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84983474970}


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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. A. K. Oblaukhov, “O maksimalnykh metricheski regulyarnykh mnozhestvakh”, PDM. Prilozhenie, 2017, no. 10, 23–24  mathnet  crossref
    2. A. V. Kutsenko, “The Hamming distance spectrum between self-dual Maiorana–McFarland bent functions”, J. Appl. Industr. Math., 12:1 (2018), 112–125  mathnet  crossref  crossref  elib
    3. A. V. Kutsenko, “O nekotorykh svoistvakh samodualnykh bent-funktsii”, PDM. Prilozhenie, 2018, no. 11, 44–46  mathnet  crossref  elib
    4. A. K. Oblaukhov, “Nizhnyaya otsenka moschnosti naibolshego metricheski regulyarnogo podmnozhestva buleva kuba”, PDM. Prilozhenie, 2018, no. 11, 14–16  mathnet  crossref  elib
    5. A. K. Oblaukhov, “Maximal metrically regular sets”, Sib. Electron. Math. Rep., 15 (2018), 1842–1849  mathnet  crossref  mathscinet  zmath  isi
    6. A. Oblaukhov, “A lower bound on the size of the largest metrically regular subset of the boolean cube”, Cryptogr. Commun., 11:4 (2019), 777–791  crossref  mathscinet  zmath  isi  scopus
    7. A. V. Kutsenko, “O metricheskikh svoistvakh mnozhestva samodualnykh bent-funktsii”, PDM. Prilozhenie, 2020, no. 13, 21–27  mathnet  crossref
  • Дискретный анализ и исследование операций
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