In this paper, we consider two classes of permutation trinomials with Niho-type exponents over the finite field ${\mathbb{F}}_{2^{2m}}$. Some sufficient conditions are obtained to characterize the coefficients of the permutation trinomials. Our numerical result suggests that those sufficient conditions for one class are also necessary.

中文翻译：

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具有偶数特征的有限域上具有Niho指数的两类置换三项式

在本文中，我们考虑有限域上具有Niho型指数的两类置换三项式 ${\mathbb{F}}_{2^{2米}}$。获得了一些足够的条件来表征置换三项式的系数。我们的数值结果表明，一类的那些充分条件也是必要的。