Cyclic types of families of polylinear recurrent sequences and generators of pseudorandom numbers

We investigate the approach to the construction of the generator of pseudorandom sequences by means of an automaton realizing the family of polylinear recurrent sequences. As characteristics describing potentially possible periods of output sequences of such generator we consider the cyclic type and the function of periods. Descriptions of these characteristics for families of geometric, arithmetic and congruent polylinear sequences over finite field are provided.