### 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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