标题： 四类新的置换三项式及其复合逆 显示英文标题

标题： Four new classes of permutation trinomials and their compositional inverses

摘要： 我们构造了四类新的有限域偶特征三次扩张上的置换三元式。 此外，我们显式地提供了每类置换三元式的多项式形式的复合逆。 另外，我们推导出了由 Xie, Li, Xu, Zeng, and Tang (2023) 最初提出的置换三元式$\alpha X^{q(q^2 - q + 1)} + \beta X^{q^2 - q + 1} + 2X$在$\alpha = 1$和$\beta = 1$条件下的复合逆。 显示英文摘要

摘要： We construct four new classes of permutation trinomials over the cubic extension of a finite field with even characteristic. Additionally, we explicitly provide the compositional inverse of each class of permutation trinomials in polynomial form. Furthermore, we derive the compositional inverse of the permutation trinomial $\alpha X^{q(q^2 - q + 1)} + \beta X^{q^2 - q + 1} + 2X$ for $\alpha = 1$ and $\beta = 1$, originally proposed by Xie, Li, Xu, Zeng, and Tang (2023).