Primitive polynomials and word oriented linear feedback shift registers

Through a large number of experiments, an explicit formula was proposed for the number of primitive σ-LFSRs over finite field, which generalized a known formula for the number of primitive LFSRs over finite field, and also was the extension of the number of primitive polynomial.Utilizing the given methods to distinguish the primitive σ-LFSR, the conjecture in three special cases was proved and a preliminary analysis for the general case was given.