Primitive Normal Polynomials Over Finite Fields

DOI10.2307/2153296zbMath0805.11083OpenAlexW2056319099MaRDI QIDQ4317674

Ilene H. Morgan, Gary L. Mullen

Publication date: 20 December 1994

Full work available at URL: https://doi.org/10.2307/2153296

zbMATH Keywords

finite fieldsminimal weightprimitive normal basisdistribution of primitive normal polynomialsprimitive normal basis theoremtables of primitive normal polynomials

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30) Algebraic number theory computations (11Y40) Software, source code, etc. for problems pertaining to number theory (11-04)

Related Items (10)

On the existence for some special primitive elements in finite fields ⋮ Primitive normal polynomials with the first two coefficients prescribed: a revised \(p\)-adic method ⋮ Division of trinomials by pentanomials and orthogonal arrays ⋮ Primitive normal polynomials with the last half coefficients prescribed ⋮ On the existence of some specific elements in finite fields of characteristic 2 ⋮ Gauss periods: orders and cryptographical applications ⋮ Primitive normal polynomials with multiple coefficients prescribed: an asymptotic result ⋮ Primitive normal bases for towers of field extensions ⋮ Primitive normal polynomials with the specified last two coefficients ⋮ Primitive normal polynomials with a prescribed coefficient

Cites Work

• Primitive elements and polynomials with arbitrary trace
• Optimal normal bases in \(GF(p^ n)\)
• Computational problems in the theory of finite fields
• Normal generators of finite fields
• On primitive and free roots in a finite field
• Optimal normal bases
• Arithmetic operations in \(GF(2^ m)\)
• Constructing normal bases in finite fields
• The generation of rimitive olynomials in GF(q) with independent roots and their applications for ower residue codes, VLSI testing and finite field multipliers using normal basis
• Searching for Primitive Roots in Finite Fields
• Primitive Polynomials Over Finite Fields
• Some Primitive Polynomials of the Third Kind
• Factoring Polynomials over Finite Fields Using Differential Equations and Normal Bases
• Primitive Normal Bases for Finite Fields
• Bases for Finite Fields
• Primitive Roots in a Finite Field
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