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 φ ( x ) = φ 0 m ( x ) φ 1 ( x ) , where φ 0 ( x ) and φ 1 ( x ) are primitive polynomials respectively raised to the power of m 1 and m 1 , m 0 · m + m 1 = 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.