Limit theorems on the normal distribution for the number of solutions of nonlinear inclusions

For a given subset $B$ of linear space $K^T$ over the field $K=GF(2)$ we study the distribution of the number $\xi$ of solutions of the system formed by inclusions $A_1x+A_2f(x)\in B$, $ x\in K^n\backslash \{0^n\}$, where $A_1$ and $A_2$ are random $T\times n$ and $T\times m$ matrices over $K$ with independend elements and $f(x)=$ $(f_1 (x),\ldots,f_m (x))\colon K^{n}\longrightarrow K^{m}$ is a given nonlinear mapping. Sufficient conditions for the convergence of distribution of $\xi$ to the standard normal distribution are obtained.