  First we study some properties of the modular group algebra
$\mathbb{F}_{p^r}[G]$ where $G$ is the additive group of a Galois ring of
characteristic $p^r$ and $\mathbb{F}_{p^r}$ is the field of $p^r$ elements.
Secondly a description of the Generalized Reed-Muller codes over
$\mathbb{F}_{p^r}$ in $\mathbb{F}_{p^r}[G]$ is presented.
