  A group code structure of a linear code is a description of the code as
one-sided or two-sided ideal of a group algebra of a finite group. In these
realizations, the group algebra is identified with the ambient space, and the
group elements with the coordinates of the ambient space. It is well known that
every affine-invariant code of length $p^m$, with $p$ prime, can be realized as
an ideal of the group algebra $\F\I$, where $\I$ is the underlying additive
group of the field with $p^m$ elements. In this paper we describe all the group
code structures of an affine-invariant code of length $p^m$ in terms of a
family of maps from $\I$ to the group of automorphisms of $\I$.
