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Dickson Polynomials Over Finite Fields and Complete Mappings

Published online by Cambridge University Press:  20 November 2018

Gary L. Mullen  and
Harald Niederreiter
Gary L. Mullen
Affiliation:
Department of Mathematics, The Pennsylvania State UniversityUniversity Park, PA 16802, U.S.A.
Harald Niederreiter
Affiliation:
Mathematical Institute Austrian Academy of SciencesD R. Ignaz-Seipel-Platz 2 A-1010ViennaAustria
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Abstract

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Dickson polynomials over finite fields are familiar examples of permutation polynomials, i.e. of polynomials for which the corresponding polynomial mapping is a permutation of the finite field. We prove that a Dickson polynomial can be a complete mapping polynomial only in some special cases. Complete mapping polynomials are of interest in combinatorics and are defined as polynomials f(x) over a finite field for which both f(x) and f(x) + x are permutation polynomials. Our result also verifies a special case of a conjecture of Chowla and Zassenhaus on permutation polynomials.

Keywords

12C05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 19 - 27
Copyright
Copyright © Canadian Mathematical Society 01

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