Geodesic
Dickson Polynomials Over Finite Fields and Complete Mappings
Canadian mathematical bulletin, Tome 30 (1987) no. 1, pp. 19-27

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1987-003-3
Mots-clés : 12C05 
Mullen, Gary L.; Niederreiter, Harald. Dickson Polynomials Over Finite Fields and Complete Mappings. Canadian mathematical bulletin, Tome 30 (1987) no. 1, pp. 19-27. doi: 10.4153/CMB-1987-003-3
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