Generalized reciprocals, factors of Dickson polynomials and generalized cyclotomic polynomials over finite fields

Authors:
Robert W. Fitzgerald;Joseph L. Yucas
Affiliations:
Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, USA;Department of Mathematics, Southern Illinois University, Carbondale, IL 62901, USA
Venue:
Finite Fields and Their Applications
Year:
2007

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Abstract

We give new descriptions of the factors of Dickson polynomials over finite fields in terms of cyclotomic factors. To do this generalized reciprocal polynomials are introduced and characterized. We also study the factorization of generalized cyclotomic polynomials and their relationship to the factorization of Dickson polynomials.