On codes that are invariant under the affine group. (Q1953326)

Let \(k[V]\) be the space of functions from a finite vector space into the algebraically closure of its field of scalars. This paper concerns the vector space \(k[V]\) of functions from a finite vector space to an algebraically closed field of the same characteristic and its \(k\mathrm{AGL}(V)\)-submodules, the subspaces which are invariant under the natural action of the affine group \(\mathrm{AGL}(V)\). This paper gives an explicit description of the \(k\mathrm{AGL}(V)\)-submodules of \(k[V]\), using the standard coordinates on \(V\), as well as a combinatorial description of the lattice of submodules.