Dembowski-Ostrom polynomials from Dickson polynomials

Authors:
Robert S. Coulter;Rex W. Matthews
Affiliations:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA;6 Earl St., Sandy Bay, Tasmania 7005, Australia
Venue:
Finite Fields and Their Applications
Year:
2010

Citing 6
Cited 1

Planar Functions and Planes of Lenz-Barlotti Class II

Designs, Codes and Cryptography
The MAGMA algebra system I: the user language

Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
A family of skew Hadamard difference sets

Journal of Combinatorial Theory Series A
Pseudo-Paley graphs and skew Hadamard difference sets from presemifields

Designs, Codes and Cryptography
Permutation Properties of Chebyshev Polynomials of the Second Kind over a Finite Field

Finite Fields and Their Applications
On the Permutation Behaviour of Dickson Polynomials of the Second Kind

Finite Fields and Their Applications

Further results on planar DO functions and commutative semifields

Designs, Codes and Cryptography

Quantified Score

Hi-index	0.00

Visualization

Abstract

Motivated by several recent results, we determine precisely when F"k(X^d,a)-F"k(0,a) is a Dembowski-Ostrom polynomial, where F"k(X,a) is a Dickson polynomial of the first or second kind. As a consequence, we obtain a classification of all such polynomials which are also planar; all examples found are equivalent to previously known examples.