On the Properties of the Minimal Polynomial of -LFSR Sequence

-Linear Feedback Shift Register (-LFSR) is a word-oriented feedback shift register, which has a better tradeoff between the security and efficiency. The sequence generated by -LFSR is called the -linear recurrence sequence and its characteristic polynomial is the matrix polynomial over finite field. With analysis of the algebra structure of the matrix polynomial ring over finite field, the sufficient and necessary condition for the minimal polynomial of -linear recurrence sequence to be unique is given.