On the Cycle Structure of Some Nonlinear Feedback Shift Registers

In this paper, we partly determine the cycle structure of two types of Nonlinear feedback shift registers (NFSRs). Based on these results, the cycle structure of a class of NFSRs with symmetric feedback functions can be completely characterized. Furthermore, an alternative proof of Kjeldsen's results is presented. Compared with the original proof based on abstract algebra theory, ours is straightforward and easy to understand.