Permutation polynomials and applications to coding theory

We present different results derived from a theorem stated by Wan and Lidl [Permutation polynomials of the form x(r) f(x((q-1)/d)) and their group structure, Monatsh. Math. 112(2) (1991) 149-163] which treats specific permutations on finite fields. We first exhibit a new class of permutation binomials and took at some interesting subclasses. We then give an estimation of the number of permutation binomials of the form X-r(X(q-1)/m +a) for a is an element of F-q(*). Finally we give applications in coding theory mainly related to a conjecture of Helleseth. (c) 2005 Elsevier Inc. All rights reserved.