Permutation polynomials over finite fields constitute an active research area and have important applications in many areas of science and engineering. In this paper, several classes of permutation polynomials with trace functions are presented over \(\mathbb {F}_{p^{n}} (p=2, 3)\) by investigating the number of solutions to special equations.

中文翻译：

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$$\mathbb {F}_{p^n}$$ F pn 上具有迹函数的几类置换多项式

有限域上的置换多项式构成了一个活跃的研究领域，在科学和工程的许多领域都有重要的应用。在本文中，通过研究特殊方程的解数，在\(\mathbb {F}_{p^{n}} (p=2, 3)\)上提出了几类具有迹函数的置换多项式。