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Mat. Vopr. Kriptogr., 2014, Volume 5, Issue 1, Pages 73–83 (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

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.

DOI: https://doi.org/10.4213/mvk107

Full text: PDF file (118 kB)
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Document Type: Article
UDC: 519.212.2
Received 26.XII.2012

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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    This publication is cited in the following articles:
    1. V. G. Mikhailov, “Formuly dlya odnoi kharakteristiki sfer i sharov v dvoichnykh prostranstvakh bolshoi razmernosti”, Diskret. matem., 30:2 (2018), 62–72  mathnet  crossref  elib
  • Математические вопросы криптографии
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