# More new classes of permutation trinomials over $\mathbb{F}_{2^n}$

## TL;DR

This paper introduces six new classes of permutation trinomials over finite fields of characteristic two, expanding the known set of such polynomials with explicit formulas and solution methods.

## Contribution

The paper provides explicit forms and solution techniques for six new classes of permutation trinomials over _{2^n}, enhancing the understanding of permutation polynomials in finite fields.

## Key findings

- Six new classes of permutation trinomials over _{2^n} identified
- Explicit formulas for these permutation trinomials derived
- Solutions of key equations determined for polynomial construction

## Abstract

Permutation polynomials over finite fields have wide applications in many areas of science and engineering. In this paper, we present six new classes of permutation trinomials over $\mathbb{F}_{2^n}$ which have explicit forms by determining the solutions of some equations.