Niho exponents have found important applications in sequence design, coding theory, and cryptography. Determining the differential spectrum of a power function with Niho exponent is a topic of considerable interest. In this paper, we investigate the power function $F(x) = x^{3q - 2}$ over $\mathbb{F}_{q^2}$, where $q = 2^m$ and $m\geq 4$ is an even integer. Notably, the exponent $3q - 2$ is a Niho exponent. By analyzing the properties of certain polynomials over $\mathbb{F}_{q^2}$, we determine the differential spectrum of $F$. Our results show that $F$ is locally differentially $4$-uniform, which complements existing results on the differential spectra of power functions with Niho exponents.

翻译：Niho指数在序列设计、编码理论和密码学中具有重要应用。确定Niho指数幂函数的差分谱是一个备受关注的研究课题。本文研究有限域$\mathbb{F}_{q^2}$上的幂函数$F(x) = x^{3q - 2}$，其中$q = 2^m$且$m\geq 4$为偶数。值得注意的是，指数$3q - 2$是一个Niho指数。通过分析$\mathbb{F}_{q^2}$上某些多项式的性质，我们确定了$F$的差分谱。研究结果表明，$F$是局部差分一致度为$4$的函数，这一结果补充了现有关于Niho指数幂函数差分谱的研究成果。