Completely normal elements in iterated quadratic extensions of finite fields

DOI10.1006/FFTA.1996.0167zbMath0952.11028OpenAlexW2026150289WikidataQ57918033 ScholiaQ57918033MaRDI QIDQ1266428

Robin J. Chapman

Publication date: 14 August 2000

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

Full work available at URL: https://doi.org/10.1006/ffta.1996.0167

zbMATH Keywords

finite fieldcomplete normal basisquadratic extensionnormal basisGalois field

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Finite fields (field-theoretic aspects) (12E20) Symbolic dynamics (37B10)

Related Items (10)

Generalized reciprocals, factors of Dickson polynomials and generalized cyclotomic polynomials over finite fields ⋮ Iterated constructions of irreducible polynomials over finite fields with linearly independent roots ⋮ Irreducible compositions of polynomials over finite fields of even characteristic ⋮ High order elements in finite fields arising from recursive towers ⋮ Irreducible compositions of polynomials over finite fields ⋮ Recursive constructions of N-polynomials over \(\text{GF}(2^s)\) ⋮ Factors of Dickson polynomials over finite fields. ⋮ Iterated constructions of completely normal polynomials ⋮ Recurrent methods for constructing irreducible polynomials over \(\mathbb F_q\) of odd characteristics. II ⋮ Explicit theorems on generator polynomials

Cites Work

• Specific irreducible polynomials with linearly independent roots over finite fields
• Eine Verschärfung des Satzes von der Normalbasis. (An improvement of the normal basis theorem)
• The explicit construction of irreducible polynomials over finite fields
• Explicit N-polynomials of \(2\)-power degree over finite fields. I

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