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This article is cited in 4 scientific papers (total in 4 papers)
Limit theorems for the number of nonzero solutions of a system of random equations over the field $\mathrm{GF}(2)$
V. G. Mikhailov
Abstract:
We study the properties of the number $\nu$ of non-zero
solutions of system of random equations over $\mathrm{GF}(2)$ with the left-hand
sides which are products of expressions of the form $a_{t1}x_1+\ldots+a_{tn}x_n+a_t$ with
independent equiprobable coefficients. The right-hand
sides of the system are zeros. We derive inequalities for
the factorial moments of the random variable $\nu$ and necessary
and sufficient conditions of the validity of the Poisson limit
theorem for $\nu$.
The research was supported by the Russian Foundation for Basic Research,
grants 99–01–00012 and 96–15–96092.
Received: 24.12.1999
Citation:
V. G. Mikhailov, “Limit theorems for the number of nonzero solutions of a system of random equations over the field $\mathrm{GF}(2)$”, Diskr. Mat., 12:1 (2000), 70–81; Discrete Math. Appl., 10:2 (2000), 115–126
Linking options:
https://www.mathnet.ru/eng/dm318https://doi.org/10.4213/dm318 https://www.mathnet.ru/eng/dm/v12/i1/p70
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