Linear Recurrences over a Finite Field with Exactly Two Periods

Ghurumuruhan Ganesan

Published 2021-03-01Version 1

In this paper, we study the periodicity structure of finite field linear recurring sequences whose period is not necessarily maximal and determine necessary and sufficient conditions for the characteristic polynomial~\(f\) to have exactly two periods in the sense that the period of any sequence generated by~\(f\) is either one or a unique integer greater than one.