Duadic Z4-Codes

Philippe Langevin, Patrick Solé
2000 Finite Fields and Their Applications  
The structure of abelian Z -codes (and more generally Z N K -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 Z codes are considered, constructed, and used to produce 4-modular lattices.
doi:10.1006/ffta.2000.0285 fatcat:shzglpcqqnb3bh75kfp3a42sku