Self-Dual Codes over the Integers Modulo 4

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 analogous 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 selfdual codes of length n ≤ 9. We also classify those self-orthogonal codes that are generated by words of type ±1 0 − 4 .