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2021 Period sets of linear recurrences over finite fields and related commutative rings
Michael R. Bush, Danjoseph Quijada
Involve 14(3): 361-376 (2021). DOI: 10.2140/involve.2021.14.361

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 𝔽 q 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 𝔽 q 1 𝔽 q r .

Citation

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Michael R. Bush. Danjoseph Quijada. "Period sets of linear recurrences over finite fields and related commutative rings." Involve 14 (3) 361 - 376, 2021. https://doi.org/10.2140/involve.2021.14.361

Information

Received: 11 May 2018; Accepted: 19 February 2021; Published: 2021
First available in Project Euclid: 30 July 2021

Digital Object Identifier: 10.2140/involve.2021.14.361

Subjects:
Primary: 11B50
Secondary: 11B37 , 11B39 , 94A55

Keywords: characteristic polynomial , cyclic group algebra , finite commutative ring , finite field , linear recurrence , period , Sequence

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 3 • 2021
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