In this paper, we investigate self-dual codes over finite rings, specifically the ring ℤ2m of integers modulo 2m. Type II codes over ℤ2m are introduced as self-dual codes with Euclidean weights which are a multiple of 2m+1. We describe a relationship between Type II codes and even unimodular lattices. This relationship provides much information on Type II codes. Double circulant Type II codes over ℤ2m are also studied.
- Double circulant code
- Even unimodular lattice
- Self-dual code over finite ring
- Type ii code