Shadow lattices and shadow codes Original Research Article

Recently shadows of unimodular lattices have been defined to derive upper bounds on the minimum norm of Type~I lattices. In this paper we study shadows of lattices mostly to construct unimodular lattices in higher dimensions. We introduce shadow-optimal lattices which are a class of optimal Type I lattices by investigating theta series of optimal Type~I lattices. These lattices are used to construct unimodular lattices by the above construction. An analogy between self-dual codes over the ring Z2k of integers and unimodular lattices is found. We also study shadow codes for Type~I codes over Z2k by considering shadow lattices.