On some classes of nonlinear shift registers with the same cyclic structure

The paper is devoted to investigating the cyclic structure of an autonomous automaton R(t) = R(Gn , δ ƒ) named a shift register with feedback function ƒ, ƒ : Gn → G, and transition function δ ƒ (y 1, y 2, . . . , yn ) = (y 2, y 3, . . . , yn , ƒ(y 1, y 2, . . . , yn )). An important problem in this field of investigation consists of constructing a nonlinear automaton R(ƒ) of a given cyclic structure, in particular, possessing a cycle of length 2 n or 2 n – 1.