Representing Maximal Pseudo-Random Sequences on the Basis of Non-Linear Vector-Valued Complication Function over a Finite Field

An automaton model of representing the nonlinear pseudo-random sequences of period L = 2
ⁿ
has been proposed. An automaton output function is defined as a non-linear complication function implementing the vector single-value transformation of automaton states on the basis of a system of non-linear modular operations in modulo belonging to the set of Fermat primes. The measure of the ensemble of sequences depends on the number of h primitive roots in the Fermat number modulo and estimated by the h! value.