ABSTRACT
The feedback shift register (FSR) is used to create pseudo-random sequences in many fields, such as cell phones and digital cable, secure and privacy communications, error detecting and correcting codes, and cryptographic systems. First, FSR is analyzed via Boolean network. FSR is regarded as a special Boolean network and the dynamic equations of FSR is converte into an equivalent algebraic equation by using semi-tensor product of matrices and matrix expression of logic. Based on them, some novel and generalized techniques are proposed to study FSR. Then, the multi-value FSR is investigated and a new method is presented to analyze its non-singularity, number of cycles, and cycle decomposition and synthesis.
