The Cycle Structure of LFSR with Arbitrary Characteristic Polynomial   over Finite Fields
  We determine the cycle structure of linear feedback shift register with arbitrary monic characteristic polynomial over any finite field. For each cycle, a method to find a state and a new way to represent the state are proposed. 
Zuling Chang, Martianus Frederic Ezerman, San Ling and Huaxiong Wang
cs.IT math.IT