 Completion at an irreducible polynomial over a finite field

For an irreducible polynomial $h\in {\mathbb{F}}_p[t]$ of degree $d$, the $h$-adic completion of ${\mathbb{F}}_p(t)$ is isomorphic to ${\mathbb{F}}_{p^d}((T))$. Its residue field is ${\mathbb{F}}_p[t]/(h)$ and $h$ is a uniformizer.