A note on short vectors in lattices from function fields

We discuss some properties of the lattices Λ which are associated to function fields over finite fields. In particular we are interested in the lattice vectors of minimum length in Λ and in the sublattice Δ⊆ΛΔ⊆Λ which is generated by these vectors. In the literature, one finds several examples of function fields where Δ and Λ have the same rank (well-rounded lattices). In this paper we construct some interesting classes of function fields with rank(Δ)