Cyclic codes and quadratic residue codes over Z₄

摘要

We prove that any Z₄-cyclic code has generators of theform (fh, 2fg) where fgh=xn-1 over Z₄. From thiswe can easily find the order of the code and generators of the dual. Aparticular interesting family of Z₄-cyclic codes arequadratic residue codes. We define such codes in terms of theiridempotent generators and show that these codes also have many goodproperties which are analogous in many respects to properties ofquadratic residue codes over a field