Primitive element pairs with a prescribed trace in the cubic extension of a finite field

Andrew R Booker, Stephen Cohen, Nicol Leong, Tim Trudgian

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
21 Downloads (Pure)

Abstract

We prove that for any prime power q∉{3,4,5} , the cubic extension Fq3 of the finite field Fq contains a primitive element ξ such that ξ+ξ−1 is also primitive, and TrFq3/Fq(ξ)=a for any prescribed a∈Fq . This completes the proof of a conjecture of Gupta et al. [‘Primitive element pairs with one prescribed trace over a finite field’, Finite Fields Appl.54 (2018), 1–14] concerning the analogous problem over an extension of arbitrary degree n≥3 .
Original languageEnglish
Pages (from-to)458-462
Number of pages5
JournalBulletin of the Australian Mathematical Society
Volume106
Issue number3
Early online date25 Apr 2022
DOIs
Publication statusE-pub ahead of print - 25 Apr 2022

Bibliographical note

Funding Information:
T. Trudgian was supported by Australian Research Council Future Fellowship FT160100094.

Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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