More classes of permutation trinomials with Niho exponents

Abstract

This paper presents two classes of permutation trinomials with the form $x^{s(2^{m}-1)+ 1}+x^{t(2^{m}-1)+ 1}+x$ over the finite field $ \mathbb {F}_{2^{2m}}$ as a supplement of the recent works of Li and Helleseth, and a class of permutation trinomials like this form over $ \mathbb {F}_{3^{2m}}$ . Moreover, we give a method to construct permutation polynomials from known ones.