On Codes that are Invariant under the Affine Group

Abstract

Let $k[V]$ be the space of functions from a finite vector space into the algebraically closure of its field of scalars. This paper describes the lattice of subspaces of $k[V]$ which are invariant under the affine group ${\mathrm AGL}(V)$. The description provides a simple method for finding the submodule generated by any set of functions given as polynomials in the standard coordinates.