Linear Recurrences over a Finite Field with Exactly Two Periods

03/01/2021

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by   Ghurumuruhan Ganesan, et al.

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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.