ML-sequences over rings z=(2e): I. constructions of nondegenerative ML-sequences II. injectivness of compression mappings of new classes

Abstract

Pseudorandom binary sequences derived from the ML-sequences over the integer residue ring Z=(2e) are proposed and studied in [1-10]. This paper is divided into two parts. The rst part is on the nondegenerative ML-sequences. In this part the so-called quasi-period of a ML-sequence is introduced, and it is noted that a ML-sequence may degenerate in the sense that it has the quasi-period shorter than its period, and the problem of constructing the nondegenerative ML-sequences is solved by giving a criterion for nondegenerative primitive polynomials. In the second part, based on the constructions [1, 6, 7] of some classes of injective mappings which compress ML-sequences over rings to binary sequences, some new classes of the injective compression mappings are proposed and proved.