A List of Maximum Period NLFSRs

Non-Linear Feedback Shift Registers (NLFSRs) are a generalization of Linear Feedback Shift Registers (LFSRs) in which a current state is a nonlinear function of the previous state. While the theory behind LFSRs is wellunderstood, many fundamental problems related to NLFSRs remain open. Probably the most important one is finding a systematic procedure for constructing NLFSRs with a guaranteed long period. Available algorithms either consider some special cases, or are applicable to small NLFSRs only. In this paper, we present a complete list of n-bit NLFSRs with the period 2 − 1, n < 25, for three different types of feedback functions with algebraic degree two. We hope that the presented experimental data might help analysing feedback functions of maximum-period NLFSRs and finding a supporting theory characterizing them.