Vol. 14, No. 3, 2021

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Period sets of linear recurrences over finite fields and related commutative rings

Michael R. Bush and Danjoseph Quijada

Vol. 14 (2021), No. 3, 361–376
Abstract

After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over 𝔽q generated by linear recurrences for a fixed choice of the degree k in the range 1 k 4. We also investigate the periods of sequences generated by linear recurrences over rings of the form 𝔽q1 𝔽qr.

Keywords
sequence, linear recurrence, period, characteristic polynomial, finite field, finite commutative ring, cyclic group algebra
Mathematical Subject Classification 2010
Primary: 11B50
Secondary: 11B37, 11B39, 94A55
Milestones
Received: 11 May 2018
Revised: 28 January 2021
Accepted: 19 February 2021
Published: 17 July 2021

Communicated by Filip Saidak
Authors
Michael R. Bush
Department of Mathematics
Washington and Lee University
Lexington, VA
United States
Danjoseph Quijada
Department of Mathematics
University of Southern California
Los Angeles, CA
United States