Permutation binomials

Abstract

A polynomial f over a finite feld F is a permutation polynomial if the mapping F→F defined by f is one-to-one. We are concerned here with binomials, that is, polynomials of the shape f=aXi+bXj+c, i>j≥1. Even in this restricted setting, it is impossible to give general necessary and sufficient conditions on a, b, c for f to be a permutation polynomial. We review, and systematize, what is known.

Keywords

• permutation polynomials
• finite fields
• binomials.