Jordan forms and nth order linear recurrences

Let p be a prime number with p ¹ 2. We consider sequences generated by nth order linear recurrence relations over the finite field Z_p. In the first part of this paper we generalize some of the ideas in 6. to nth order linear recurrences. We then consider the case where the characteristic polynomial of the recurrence has one root in Z_p of multiplicity n. In this case, we show that the corresponding recurrence can be generated by a relatively simple matrix.