Convergence rate estimators for the number of ones in outcome sequence of MCV generator with $m$-dependent registers items

This paper is focused on studying properties of the number of ones $\xi_{r}$ in outcome sequence of MCV generator with $r$ registers over $GF(2).$ We concern on the case when generator outcome sequence has length close to the cycle length and registers filled with $m$-dependent binary random variables. Exact expressions for mean and variance of ${{\xi }_{r}}$ are given. We derive estimate in uniform metric between cumulative distribution functions of the standardized number of ones in MCV generator outcome sequence and product of $r$ independent standard normal random variables. The estimate allows to prove limit theorem for ${{\xi }_{r}}$ when number $r$ is fixed. We also estimate distance (in uniform metric) between the cumulative distribution function of normalized $\xi_{r}$ and log-normal distribution law. This result allows to prove a normal-type limit theorem for $r\to \infty$.