Primitive normal bases with prescribed trace
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Publication:1293965
DOI10.1007/S002000050112zbMath0931.12002OpenAlexW2067032769MaRDI QIDQ1293965
Dirk Hachenberger, Stephen D. Cohen
Publication date: 2 March 2000
Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)
Full work available at URL: https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/1005
Exponential sums (11T23) Finite fields (field-theoretic aspects) (12E20) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)
Related Items (23)
On the existence for some special primitive elements in finite fields ⋮ On the existence of primitive completely normal bases of finite fields ⋮ Primitive normal polynomials with the first two coefficients prescribed: a revised \(p\)-adic method ⋮ Primitive free cubics with specified norm and trace ⋮ Normal bases and primitive elements over finite fields ⋮ Variations of the primitive normal basis theorem ⋮ Primitive normal polynomials with the last half coefficients prescribed ⋮ Self-reciprocal irreducible polynomials with prescribed coefficients ⋮ On the existence of some specific elements in finite fields of characteristic 2 ⋮ Existence and properties of \(k\)-normal elements over finite fields ⋮ Primitive normal polynomials with multiple coefficients prescribed: an asymptotic result ⋮ Existence of primitive 1-normal elements in finite fields ⋮ An extension of the (strong) primitive normal basis theorem ⋮ Normal bases over \(\text{GF}(q)\) ⋮ Primitive normal bases for towers of field extensions ⋮ Characterizing Normal Bases via the Trace Map ⋮ Primitive normal pairs with prescribed norm and trace ⋮ A generalization of the Hansen-Mullen conjecture on irreducible polynomials over finite fields ⋮ Primitive normal polynomials with the specified last two coefficients ⋮ Explicit theorems on generator polynomials ⋮ Further results on the Morgan-Mullen conjecture ⋮ Primitive normal polynomials with a prescribed coefficient ⋮ Generators for primary closures of Galois fields.
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