A New Effective Shift Rule for M-Sequences

Pseudo-random sequences have been extensively used in design theory, coding theory, and cryptographic system. Pseudo-random sequences generator based on feedback shift register is an important component of a symmetric crypto-system, which is circuit equipment consisting of consecutive binary storage units regulated by a clock. As a class of important pseudo-random sequences, the M-sequences plays an important role in the systems of cryptography and communication. In this paper, a novel combinatorial method is proposed to construct -length strings. This new construction method, the semi-prefer- XOR shift rule, is based on the structure of the induced digraphs of some shift operators. Thus, a large class of M-sequences is provided.