  Let $\mathcal{M}$ be the Artin-Mumford curve over the finite prime field
$\mathbb{F}_p$ with $p>2$. By a result of Valentini and Madan,
$\mbox{Aut}_{\mathbb{F}_p}(\mathcal{M})\cong H$ with $H=(C_p\times C_p)\rtimes
D_{p-1}$. We prove that if $\mathcal{X}$ is an algebraic curve of genus
$g=(p-1)^2$ such that $\mbox{Aut}_{\mathbb{F}_p}(\mathcal{X})$ contains a
subgroup isomorphic to $H$ then $\mathcal{X}$ is birationally equivalent over
$\mathbb{F}_p$ to the Artin-Mumford curve $\mathcal{M}$.
