Necessities and sufficiencies of a class of permutation polynomials over finite fields

Abstract

For the finite field ${\mathbb{F}}_{2^{3m}}$, permutation polynomials of the form $(x^{2^m}+x+\delta {)}^s+cx$ are studied. Necessary and sufficient conditions are given for the polynomials to be permutation polynomials. For this, the structures and properties of the field elements are analyzed.