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.
- Self-dual codes
- Unimodular lattices
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics