Pseudo-random sequences with non-maximal length realized according to the Galois scheme based on the primitive polynomial in degree

Abstract

Abstract We consider homogeneous and nonhomogeneous pseudo-random sequences of non-maximal length formed by Galois generator based on characteristic polynomial in degree. We discovered periodic polynomial structures in degree in general form and on characteristic examples. We presented and applied the decimation method of periodic sequences, giving their decomposition on elementary M-sequences and constant components. We solved the tasks of analyzing of the diversity of generated sequences, which are organized and ordered from elements of direct and inverse M-sequences, and zero and one constants. We have obtained a general analytical relationship between decimation results and probabilistic properties. We discovered conditions for forming equal probability properties of the resulting sequences and determined the boundary relations of the generator parameters with the initial task of the minimum order of elementary M-sequences.