Geodesic
Formulas for a characteristic of spheres and balls in binary high-dimensional spaces
Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 62-72.

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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. 
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V. G. Mikhailov. Formulas for a characteristic of spheres and balls in binary high-dimensional spaces. Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 62-72. http://geodesic.mathdoc.fr/item/DM_2018_30_2_a5/

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