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Mat. Vopr. Kriptogr., 2011, Volume 2, Issue 1, Pages 29–73 (Mi mvk25)  

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

Basises of integers under the multiplace shift operations

F. M. Malyshev

Academy of Cryptography of Russian Federation, Moscow

Abstract: A notion of $(k,m)$-basis of $\mathbb Z$ is defined for integers $k,m$ ($0<k<m$, $(k,m)=\nobreakspace1$). Its definition uses an extension operation: a subset $U\subset\mathbb Z$ may be extended to $U\cup\{i,i+k,i+m\}$ if $|U\cap\{i,i+k,i+m\}|=2$ for some $i\in\mathbb Z$. A minimal subset $S\subset\mathbb Z$ is a $(m,k)$-basis if each $z\in\mathbb Z$ belongs to an extension of $S$ obtained by several extension operations. A structure of $(m,k)$-basises is investigated, precise bounds for the number of their elements are obtained.

Key words: integer lattices, quasigroup relations, minimal basis.

DOI: https://doi.org/10.4213/mvk25

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Document Type: Article
UDC: 512.532
Received 22.IV.2010

Citation: F. M. Malyshev, “Basises of integers under the multiplace shift operations”, Mat. Vopr. Kriptogr., 2:1 (2011), 29–73

Citation in format AMSBIB
\Bibitem{Mal11}
\by F.~M.~Malyshev
\paper Basises of integers under the multiplace shift operations
\jour Mat. Vopr. Kriptogr.
\yr 2011
\vol 2
\issue 1
\pages 29--73
\mathnet{http://mi.mathnet.ru/mvk25}
\crossref{https://doi.org/10.4213/mvk25}


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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. F. M. Malyshev, “Metricheskie svoistva vlozhenii mnozhestva tselykh chisel v tsilindr”, Matem. vopr. kriptogr., 3:3 (2012), 57–79  mathnet  crossref
    2. F. M. Malyshev, “Bazisy rekurrentnykh posledovatelnostei”, Chebyshevskii sb., 16:2 (2015), 155–185  mathnet  elib
    3. F. M. Malyshev, “Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle”, Discrete Math. Appl., 27:3 (2017), 149–176  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математические вопросы криптографии
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