The Properties of a Class of Linear FSRs and Their Applications to the Construction of Nonlinear FSRs

In this paper, the cycle structure and adjacency graphs of a class of linear feedback shift registers (LFSRs) are determined. By recursively applying the $D$ -morphism to the maximum-length LFSRs and representing the cycles by generating functions, a new family of maximum-length nonlinear feedback shift registers (NFSRs) are proposed based on the properties of these LFSRs. The number of NFSRs in the proposed family is also considered.