THE NORMAL LIMIT DISTRIBUTION OF THE NUMBER OF FALSE SOLUTIONS OF A SYSTEM OF NONLINEAR RANDOM EQUATIONS IN THE FIELD GF(2)

VOLODYMYR I. MASOL AND SVITLANA Y. SLOBODYAN

Theory of Stochastic Processes Vol. 12 (28), no. 1–2, 2006, pp. 116–126

The theorem on a normal limit $n\rightarrow\infty$ 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 $[\rho n]$, $\rho=const$, $0<\rho<1$.

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