Pseudo-random sequences of non-maximum length on shift registers with reducible and primitive polynomials
Abstract Inhomogeneous pseudo-random sequences of non-maximal length formed by shift registers with linear feedbacks based on a characteristic polynomial of degree n of the form ϕ(x)=ϕ1(x)ϕ2(x), where ϕ1(x) = x m1 ⊕ 1, and ϕ2(x) of degree m 2 is primitive (m 1 = 2 k , k is a positive integer, n = m 1 + m 2) are considered. Three schemes that are equivalent in terms of periodic sequence structures were considered. Of the greatest interest are the shift registers connected in an arbitrary way using a modulo-two adder, the feedbacks in which correspond to the multipliers ϕ1(x) and ϕ2(x) the polynomials ϕ(x). In this case, there is a complex process of forming output sequences, which involves both direct and inverse M-sequences. The statement about the singularity of the generated sequences at m 1 = 4 is proved, which is confirmed by their decimation with an index equal to the period of the primitive polynomial.
