On the existence of some specific elements in finite fields of characteristic 2

DOI10.1016/j.ffa.2012.04.003zbMath1292.11136OpenAlexW2090009046MaRDI QIDQ439089

Xiwang Cao, Pei-Pei Wang, Rong Quan Feng

Publication date: 1 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2012.04.003

zbMATH Keywords

exponential sumscharactersfinite fieldsprimitive elementnormal element

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Exponential sums (11T23) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (20)

On the existence for some special primitive elements in finite fields ⋮ Existence of some special primitive normal elements over finite fields ⋮ The primitive roots and a problem related to the golomb conjecture ⋮ Normal bases and primitive elements over finite fields ⋮ Existence of pair of primitive elements over finite fields of characteristic 2 ⋮ On the Golomb's conjecture and Lehmer's numbers ⋮ A note on the primitive roots and the Golomb conjecture ⋮ Pairs of primitive elements in fields of even order ⋮ Primitive normal values of rational functions over finite fields ⋮ On primitive normal elements over finite fields ⋮ Some estimate of character sums and its applications ⋮ Primitive values of rational functions at primitive elements of a finite field ⋮ Unnamed Item ⋮ A mean value related to primitive roots and Golomb's conjectures ⋮ Linear combinations of primitive elements of a finite field ⋮ An extension of the (strong) primitive normal basis theorem ⋮ Pair of primitive elements with prescribed traces over finite fields ⋮ Primitive element pairs with one prescribed trace over a finite field ⋮ Primitive normal pairs with prescribed norm and trace ⋮ On the existence of pairs of primitive normal elements over finite fields

Cites Work

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• On primitive polynomials over finite fields
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• On primitive elements of trace equal to 1 in GF(\(2^ m)\)
• Primitive normal bases with prescribed trace
• Primitive polynomials over finite fields of characteristic two
• Primitive polynomials with a prescribed coefficient
• Primitive polynomial with three coefficients prescribed
• Primitive Roots in the Quadratic Extension of a Finite Field
• Primitive Normal Polynomials Over Finite Fields
• Generators and irreducible polynomials over finite fields
• Gauss periods: orders and cryptographical applications
• Primitive Normal Bases for Finite Fields
• On Orders of Optimal Normal Basis Generators
• Bases for Finite Fields
• Primitive Roots in a Finite Field
• Primitive elements with zero traces

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