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Matematicheskie Voprosy Kriptografii [Mathematical Aspects of Cryptography], 2014, Volume 5, Issue 1, Pages 73–83
DOI: https://doi.org/10.4213/mvk107
(Mi mvk107)
 

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

On an asymptotical property of spheres in the discrete spaces of large dimension

V. A. Kopytceva, V. G. Mikhailovb

a Academy of Cryptography of the Russian Federation, Moscow
b Steklov Mathematical Institute of RAS, Moscow
Full-text PDF (118 kB) Citations (1)
References:
Abstract: We study an asymptotic (as $m\to\infty$) property of sets in $m$-dimensional linear spaces $K^m$ over the finite field $K$. This property is used in the conditions of Poisson type limit theorems for the number of solutions of systems of random linear equations or random inclusions over finite field. It is shown that the spheres in $K^m$ (with respect to the Hamming distance) possess this property for $m\to\infty$ if the dependence of their radii on $m$ guarantees the unbounded growth of the numbers of their elements.
Key words: linear spaces over finite fields, Hamming distance, random linear inclusions.
Received 26.XII.2012
Document Type: Article
UDC: 519.212.2
Language: Russian
Citation: V. A. Kopytcev, V. G. Mikhailov, “On an asymptotical property of spheres in the discrete spaces of large dimension”, Mat. Vopr. Kriptogr., 5:1 (2014), 73–83
Citation in format AMSBIB
\Bibitem{KopMik14}
\by V.~A.~Kopytcev, V.~G.~Mikhailov
\paper On an asymptotical property of spheres in the discrete spaces of large dimension
\jour Mat. Vopr. Kriptogr.
\yr 2014
\vol 5
\issue 1
\pages 73--83
\mathnet{http://mi.mathnet.ru/mvk107}
\crossref{https://doi.org/10.4213/mvk107}
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  • https://doi.org/10.4213/mvk107
  • https://www.mathnet.ru/eng/mvk/v5/i1/p73
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические вопросы криптографии
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    Abstract page:449
    Full-text PDF :181
    References:66
    First page:2
     
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