Self-dual codes over the integers modulo 4

Abstract

Michael Klemm has recently studied the conditions satisfied by the complete weight enumerator of a self-dual code over Z 4, the ring of integers modulo 4. In the present paper we deduce analogues theorems for the “symmetrized” weight enumerator (which ignores the difference between +1 and −1 coordinates) and the Hamming weight enumerator. We give a number of examples of self-dual codes, including codes which realize the basic weight enumerators occurring in all these theorems, and the complete list of self-dual codes of length n ⩽ 9. We also classify those self-orthogonal codes that are generated by words of type ±1 4 O n−4 .