The Weight Distributions of Two Classes of Linear Codes From Perfect Nonlinear Functions

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 $m\in {\mathbb{N}}_{+}$.