About \(r\)-primitive and \(k\)-normal elements in finite fields

DOI10.1007/s10623-022-01101-8OpenAlexW4293168095WikidataQ114226813 ScholiaQ114226813MaRDI QIDQ2678980

Victor G. L. Neumann, Josimar J. R. Aguirre, Cícero Fernandes de Carvalho

Publication date: 18 January 2023

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.13151

zbMATH Keywords

finite fieldsnormal basis\(k\)-normal element\(r\)-primitive element

Mathematics Subject Classification ID

Exponential sums (11T23) Finite fields (field-theoretic aspects) (12E20) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (5)

Pairs of \(r\)-primitive and \(k\)-normal elements in finite fields ⋮ The average density of \(k\)-normal elements over finite fields ⋮ Inverses of \(r\)-primitive \(k\)-normal elements over finite fields ⋮ On \(r\)-primitive \(k\)-normal elements with prescribed norm and trace over finite fields ⋮ r -primitive k -normal elements in arithmetic progressions over finite fields

Uses Software

• SageMath

Cites Work

• Existence of primitive 1-normal elements in finite fields
• Primitive element pairs with one prescribed trace over a finite field
• Existence of primitive 2-normal elements in finite fields
• On the existence of pairs of primitive and normal elements over finite fields
• Existence results on \(k\)-normal elements over finite fields
• Existence and properties of \(k\)-normal elements over finite fields
• A CLASS OF INCOMPLETE CHARACTER SUMS
• THE PRIMITIVE NORMAL BASIS THEOREM – WITHOUT A COMPUTER
• Primitive Normal Bases for Finite Fields
• Topics in Galois Fields

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