On the number of special feedback configurations in linear modular systems

This paper deals with a state feedback in linear modular systems (LMSs) defined over a finite field Fq. By means of a state feedback, any controllable LMS S can be converted to a closed loop system having a desired characteristic polynomial p(s). Given a polynomial p(s), we calculate the number of state feedback matrices which result in single input controllable closed loop systems having a characteristic polynomial p(s).