GENERATORS OF FINITE FIELDS WITH PRESCRIBED TRACES

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 resul...

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Bibliographic Details
Published inJournal of the Australian Mathematical Society (2001) Vol. 112; no. 3; pp. 355 - 366
Main Authors REIS, LUCAS, RIBAS, SÁVIO
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.06.2022
Subjects
Fields (mathematics)
field trace
12E20
finite fields
11T24
primitive elements
character sums
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Summary: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.
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ISSN:1446-7887
1446-8107
DOI:10.1017/S1446788721000094