Self-dual codes over rings and the Chinese remainder theorem

We give some characterizations of self-dual codes over rings, specifically the ring Z_2k, where Z_2k denotes the ring Z/2kZ of integers modulo 2k, using the Chinese Remainder Theorem, investigating Type I and Type II codes. The Chinese Remainder Theorem plays an important role in the study of self-dual codes over Z_2k when 2k is not a prime power, while the Hensel lift is a powerful tool when 2k is a prime power. In particular, we concentrate on the case k = 3 and use construction A to build unimodular and 3-modular lattices.