On permutation polynomials over finite fields /

Official URL: http://risc01.sabanciuniv.edu/record=b1164871 (Table of Contents)

A permutation polynomial (PP) over a nite eld Fq is a polynomial in Fq[x] which induces a bijective map from Fq to itself. PPs are of great theoretical interest and are also needed for applications. This thesis starts with some basic facts about PPs. Recent results about one of the most important open problems in this topic: counting PPs of a given degree, are presented. Well known classes of PPs are the linear polynomials, the monomials xk, with gcd(k, q 1) = 1, the linearized polynomials, and the Dickson polynomials. It turns out that nding new classes of PPs is not easy. We also focus on this problem and give a survey of some recent constructions.