Determination of a type of permutation binomials and trinomials

Abstract

Let $${\mathbb {F}}_q$$ denote the finite field of order q. In this paper, we determine certain permutation binomials and permutation trinomials of the form $$x^{r}h(x^{q+1})$$ over $$\mathbb {F}_{q^2}$$. Some of them are generalizations of known ones.