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GENERATORS OF FINITE FIELDS WITH PRESCRIBED TRACES

Part of: General field theory Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  27 May 2021

LUCAS REIS  and
SÁVIO RIBAS
LUCAS REIS
Affiliation:
Departamento de Matemática, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG 30270-901, Brazil
SÁVIO RIBAS
Affiliation:
Departamento de Matemática, Universidade Federal de Ouro Preto (UFOP), Ouro Preto, MG 35400-000, Brazil e-mail: savio.ribas@ufop.edu.br
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Abstract

This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result provides an inequality-like condition to ensure the existence of such elements. We then derive concrete existence results for a special class of intermediate extensions.

Keywords

character sumsfield tracefinite fieldsprimitive elements

MSC classification

Primary: 12E20: Finite fields (field-theoretic aspects)
Secondary: 11T24: Other character sums and Gauss sums

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 112 , Issue 3 , June 2022 , pp. 355 - 366
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Dzmitry Badziahin

References

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