Two classes of permutation trinomials over [formula omitted] in characteristic two

Abstract

Let q=2m and Fq3 be the finite field with q3 elements. In this paper, based on the multivariate method, resultant elimination, and transforming into dealing with some equations over finite fields, we propose two classes of permutation trinomials of Fq3. We illustrate that these two classes of permutation trinomials are QM-inequivalent to all known permutation polynomials over Fq3. Some well-known results can be covered by our theorems.