Duadic Z4-Codes

The structure of abelian Z4-codes (and more generally Zpm-codes) is studied. The approach is spectral: discrete Fourier transform and idempotents. 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 Z4 codes are considered, constructed, and used to produce 4-modular lattices.