Two types of permutation polynomials with special forms

Abstract

Let q be a power of a prime and Fq be a finite field with q elements. In this paper, we propose four families of infinite classes of permutation trinomials having the form cx−xs+xqs, and investigate the relationship between two types of widely discussed permutation polynomials. Based on this relation, many classes of permutation polynomials having the form (xqk−x+δ)s+cx without restriction on δ are derived.