Normal bases and primitive elements over finite fields

DOI10.1016/j.ffa.2013.12.002zbMath1288.11112OpenAlexW2012549780MaRDI QIDQ2637331

Giorgos Kapetanakis

Publication date: 11 February 2014

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2013.12.002

zbMATH Keywords

finite fieldcharacter sumnormal basisprimitive elementfree element

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Finite fields (field-theoretic aspects) (12E20) Other character sums and Gauss sums (11T24) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (17)

Existence of some special primitive normal elements over finite fields ⋮ On the existence of primitive completely normal bases of finite fields ⋮ On the existence of primitive normal elements of rational form over finite fields of even characteristic ⋮ The existence of primitive normal elements of quadratic forms over finite fields ⋮ On the existence of pairs of primitive and normal elements over finite fields ⋮ Existence of pair of primitive elements over finite fields of characteristic 2 ⋮ A infinite class of Kasami functions that are not APN infinitely often ⋮ Pairs of \(r\)-primitive and \(k\)-normal elements in finite fields ⋮ On arithmetic progressions in finite fields ⋮ Pair of primitive normal elements of rational form over finite fields of characteristic 2 ⋮ Primitive normal values of rational functions over finite fields ⋮ On primitive normal elements over finite fields ⋮ Unnamed Item ⋮ Existence and cardinality of \(k\)-normal elements in finite fields ⋮ An extension of the (strong) primitive normal basis theorem ⋮ Further results on the Morgan-Mullen conjecture ⋮ On the existence of pairs of primitive normal elements over finite fields

Cites Work

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• The strong primitive normal basis theorem
• THE PRIMITIVE NORMAL BASIS THEOREM – WITHOUT A COMPUTER
• Mixed exponential sums over finite fields
• Primitive Normal Bases for Finite Fields
• Bases for Finite Fields
• Primitive Roots in a Finite Field

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