A function $F:{\mathbb{F}}_{p^n}\to {\mathbb{F}}_{p^m}$, is a vectorial s-plateaued function if for each component function $F_b(\mu )=T{r}_n(bF(x)),b\in {\mathbb{F}}_{p^m}^{⁎}$ and $\mu \in {\mathbb{F}}_{p^n}$, the Walsh transform value $|\widehat{F_b}(\mu )|$ is either 0 or $p^{\frac{n+s}{2}}$. In this paper, we explore the relation between (vectorial) s-plateaued functions and partial geometric difference sets. Moreover, we establish the link between three-valued cross-correlation of p-ary sequences and vectorial s-plateaued functions. Using this link, we provide a partition of ${\mathbb{F}}_{3^n}$ into partial geometric difference sets. Conversely, using a partition of ${\mathbb{F}}_{3^n}$ into partial geometric difference sets, we construct ternary plateaued functions $f:{\mathbb{F}}_{3^n}\to {\mathbb{F}}_3$. We also give a characterization of p-ary plateaued functions in terms of special matrices which enables us to give the link between such functions and second-order derivatives using a different approach.

功能 $F：{\mathbb{F}}_{p^{ñ}}\to {\mathbb{F}}_{p^{米}}$如果是每个分量函数，则是向量s-高原函数$F_b（\mu ）=Ť{\mathrm{[R}}_{ñ}（bF（X）），b\in {\mathbb{F}}_{p^{米}}^{⁎}$ 和 $\mu \in {\mathbb{F}}_{p^{ñ}}$，沃尔什变换值 $|\widehat{F_b}（\mu ）|$ 是0或 $p^{\frac{ñ+s}{2}}$。在本文中，我们探索了（矢量）s平稳函数与部分几何差集之间的关系。此外，我们建立了p元序列的三值互相关和矢量s平稳函数之间的联系。使用此链接，我们提供了一个分区${\mathbb{F}}_{3^{ñ}}$分成部分几何差异集。相反，使用${\mathbb{F}}_{3^{ñ}}$ 分成部分几何差异集，我们构造三元平稳函数 $F：{\mathbb{F}}_{3^{ñ}}\to {\mathbb{F}}_3$。我们还根据特殊矩阵对p元平稳函数进行了表征，这使我们能够使用不同的方法给出此类函数与二阶导数之间的联系。