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 Diskr. Mat., 2018, Volume 30, Issue 2, Pages 62–72 (Mi dm1507)

Formulas for a characteristic of spheres and balls in binary high-dimensional spaces

V. G. Mikhailov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We consider a special function $\rho(H)$ of the subset $H$ of $n$-dimensional vector linear space over the field $K$. This function is used in the estimates of accuracy of the Poisson approximation for the distribution of the number of solutions of systems of random equations and random inclusions over $K$. For the case when $K=GF(2)$ and $H$ is a sphere or ball (in the Hamming metric) in $\{0,1\}^n$ we obtain explicit and approximate formulas for $\rho(H)$ for sufficiently large values of $n$.

Keywords: linear spaces over finite fields, Hamming metric, random linear inclusions.

 Funding Agency Grant Number Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01

DOI: https://doi.org/10.4213/dm1507

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English version:
Discrete Mathematics and Applications, 2019, 29:5, 311–319

Bibliographic databases:

UDC: 519.212.2

Citation: V. G. Mikhailov, “Formulas for a characteristic of spheres and balls in binary high-dimensional spaces”, Diskr. Mat., 30:2 (2018), 62–72; Discrete Math. Appl., 29:5 (2019), 311–319

Citation in format AMSBIB
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