On the number of ones in the cycle of multicycliс sequence determined by Boolean function

The paper presents formulas that denote the relationship between the number of ones in the cycle of a multicyclic sequence modulo 2, defined by the Boolean function, and the number of ones in the registers of the generator through the spectral characteristics of this function. Using these formulas, we prove normal-type limit theorems for the number of ones in the cycle of the multicyclic sequence if the registers are filled with independent binary random variables with the same distributions within each register, the lengths of the registers tend to infinity and their number remains fixed. We prove that the limit distribution can be both the usual normal distribution and the distribution of the product of independent standard normal random variables.