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 xrf(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 look at some interesting subclasses. We then give an estimation of the number of permutation binomials of the form Xr(X(q-1)/m+a) for . Finally we give applications in coding theory mainly related to a conjecture of Helleseth.