Let $q=2^m$ and ${\mathbb{F}}_{q^3}$ be the finite field with $q^3$ 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 ${\mathbb{F}}_{q^3}$. We illustrate that these two classes of permutation trinomials are QM-inequivalent to all known permutation polynomials over ${\mathbb{F}}_{q^3}$. Some well-known results can be covered by our theorems.

中文翻译：

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特征二中 Fq3 上的两类置换三项式

让$q=2^{米}$和${\mathbb{F}}_{q^3}$是有限域$q^3$元素。在本文中，基于多元方法，结果消除，并转化为处理有限域上的一些方程，我们提出了两类置换三项式：${\mathbb{F}}_{q^3}$。我们说明这两类置换三项式与所有已知的置换多项式是 QM 不等价的${\mathbb{F}}_{q^3}$。我们的定理可以涵盖一些众所周知的结果。