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We prove a result on the rate of convergence as n → ∞ of the distribution of the number of false solutions of a system of nonlinear random equations in the field GF (2) to the Poisson distribution with parameter 2m. We assume, in particular, that the difference between the number n of unknowns and the number N of equations of the system is a constant m. 1. Setting of the problem. Statement of the result Consider the following system of equations:

theory of probability and mathematical statistics

An estimate for the rate of convergence of the distribution of the number of false solutions of a system of nonlinear random equations in the field $GF(2)$