Pseudo-random sequences with nonmaximal length based on the shift register and reducible polynomial

We consider nonhomogeneous pseudorandom sequences of nonmaximal length formed by a shift register with linear feedback (Fibonacci generators), and with internal half-adders (Galois generators). As a basis, we consider characteristic polynomial raised to the power of n of a form ${\rm{\varphi }}(\rm{x})={{\rm{\varphi }}}_{0}^{m}({x}){{\rm{\varphi }}}_{1}(\rm{x})$, where φ₀ (x) and φ₁ (x) are primitive polynomials respectively raised to the power of m₁ and m₁, m₀ · m + m₁ = n. We discovered periodic polynomial structures. Examples demonstrate a diversity of generated practical sequences, which are organized and ordered from elements of direct and inverse M-sequences. We investigated probabilistic properties of the formed sequences.