Iterated constructions of irreducible polynomials over finite fields with linearly independent roots

DOI10.1016/j.ffa.2003.09.002zbMath1049.11135OpenAlexW2030799343MaRDI QIDQ596584

Melsik K. Kyureghyan

Publication date: 10 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2003.09.002

zbMATH Keywords

normal basesiterative methodsirreducible polynomials and normal polynomials (N-polynomials) over finite fieldsQ-transformationtrace-compatible sequences

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (13)

Recursive construction of normal polynomials over finite fields ⋮ Irreducible compositions of polynomials over finite fields of even characteristic ⋮ Some notes on the k-normal elements and k-normal polynomials over finite fields ⋮ Constructing irreducible polynomials recursively with a reverse composition method ⋮ On the reducibility of some composite polynomials over finite fields ⋮ Irreducible compositions of polynomials over finite fields ⋮ Recursive constructions of k-normal polynomials using some rational transformations over finite fields ⋮ A new criterion on normal bases of finite field extensions ⋮ FACTORIZATION OF SOME COMPOSITE POLYNOMIALS OVER FINITE FIELDS ⋮ On an iterated construction of irreducible polynomials over finite fields of even characteristic by Kyuregyan ⋮ A note on N-polynomials over finite fields ⋮ A correspondence of certain irreducible polynomials over finite fields ⋮ Explicit theorems on generator polynomials

Cites Work

• The explicit construction of irreducible polynomials over finite fields
• Completely normal elements in iterated quadratic extensions of finite fields
• Recurrent methods for constructing irreducible polynomials over \(\text{GF}(2^s)\)
• Explicit N-polynomials of \(2\)-power degree over finite fields. I
• Finding Isomorphisms Between Finite Fields
• CONSTRUCTION OF POLYNOMIALS IRREDUCIBLE OVER A FINITE FIELD WITH LINEARLY INDEPENDENT ROOTS
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