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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
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Abstract |
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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 generated by linear recurrences for a fixed choice of the degree in the range . We also investigate the periods of sequences generated by linear recurrences over rings of the form . |
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Keywords
sequence, linear recurrence, period, characteristic
polynomial, finite field, finite commutative ring, cyclic
group algebra
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Mathematical Subject Classification 2010
Primary: 11B50
Secondary: 11B37, 11B39, 94A55
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Milestones
Received: 11 May 2018
Revised: 28 January 2021
Accepted: 19 February 2021
Published: 17 July 2021
Communicated by Filip Saidak
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Authors |
| Michael R. Bush | |
| Department of Mathematics Washington and Lee University Lexington, VA United States |
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| Danjoseph Quijada | |
| Department of Mathematics University of Southern California Los Angeles, CA United States |
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