The normal limit distribution of the number of false solutions of a system of nonlinear random equations in the field GF(2)

Abstract

The theorem on a normal limit (n→∞) distribution of the number of false solutions of a beforehand consistent system of nonlinear random equations in the field GF(2) with independent coefficients is proved. In particular, we assume that each equation has coefficients that take values 0 and 1 with equal probability; the system has a solution where the number of ones equals [ρn], ρ = const, 0 < ρ < 1.