In this paper, we employ general results on the value distributions of perfect nonlinear functions from $\mathbb{F}_{p^m}$ to $\mathbb{F}_p$ together with a specific group action to give a unified approach to determining the weight distributions of two classes of linear codes over $\mathbb{F}_p$ constructed from perfect nonlinear functions, where $p$ is an odd prime number and $m\in\mathbb{N}_+$.

翻译：本文利用从$\mathbb{F}_{p^m}$到$\mathbb{F}_p$的完美非线性函数值分布的一般结论，并结合特定的群作用，给出了一种统一的方法来确定由完美非线性函数构造的两类$\mathbb{F}_p$上线性码的权重分布，其中$p$为奇素数，$m\in\mathbb{N}_+$。