Permutation polynomials of the type xrg(xs) over Fq2n

We provide some new families of permutation polynomials of Fq2n of the type xr g(xs), where the integers r,s and the polynomial g ∈ Fq [x] satisfy particular restrictions. Some generalizations of known permutation binomials and trinomials that involve a sort of symmetric polynomials are given. Other constructions are based on the study of algebraic curves associated to certain polynomials. In particular we generalize families of permutation polynomials constructed by Gupta–Sharma, Li–Helleseth, Li–Qu–Li–Fu.