Self-dual codes over rings and the Chinese remainder theorem

Abstract

We give some characterizations of self-dual codes over rings, specifically 1 11e ring \mathbb{Z}_{2k} , where \mathbb{Z}_{2k} denotes the ring \mathbb{Z}/2k\mathbb{Z} of integers modulo 2k , using the (i',hi11cse Remainder Theorem, investigating Type I and Type II codes The Chinese Re\prime naindt^{\backslash }t. Theorem plays an important role in the study of self-dual codes over \mathbb{Z}_{2k} when 2k is I10\{ a prime power, while the Hensel lift is a powerful tool when 2k is a prime I ) ower Ir1 particular, we concentrate on the case k=3 and use construction A to build unimodular and 3-modular lattices.