PRIMITIVE POLYNOMIALS, SINGER CYCLES, AND WORD ORIENTED LINEAR FEEDBACK SHIFT REGISTERS
Sudhir R. Ghorpade, Sartaj Ul Hasan, Meena Kumari · 2011
Abstract. Using the structure of Singer cycles in general linear groups, we prove a conjecture of Zeng, Han and He (2007) in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive σ-LFSRs of a given order over a finite field, and it generalizes a known formula for the number of primitive LFSRs, which, in turn, is the number of primitive polynomials of a given degree over a finite field. Several results and questions related to the general case of the Zeng, Han and He Conjecture are also discussed. 1.