Linearization of multi-valued nonlinear feedback shift registers

The Linearization of Nonlinear feedback shift registers (NFSRs) is to find their state transition matrices. In this paper, we investigate the linearization multi-valued NFSRs by considering it as a logical network via a semi-tensor product approach. A new state transition matrix is found for an multi-valued NFSR, which can be simply computed from the truth table of its feedback function, and the new state transition matrix is easier to compute and is more explicit. First, a linear representation of a multi-valued NFSR is given, based on which several necessary and sufficient conditions for the nonsingularity are given. Then, some properties of the state transition matrice are provided, which are helpful to theoretically analyze NFSRs. Finally, we give properties of a maximum length multi-valued NFSR and the linear representation of the general structure of an n-bit shift register with updating functions.