Duadic \(\mathbb{Z}_4\)-codes (Q1590974)

The structure of abelian \(\mathbb{Z}_4\)-codes (and more generally \(\mathbb{Z}_{p^n}\)-codes) is studied. A criterion for self-duality is derived. An arithmetic test on the length for the existence of nontrivial abelian self-dual codes is derived. A natural generalization of both the supplemented quadratic residue codes and the binary duadic codes is introduced. Isodual abelian \(\mathbb{Z}_4\)-codes are considered and used to produce \(4\)-modular lattices. Some results of this paper were generalized later by \textit{S. Ling} and \textit{P. Solé} [Appl. Algebra Eng. Commun. Comput. 12, 365-379 (2001; Zbl 1030.94041)].