Generalized Hadamard full propelinear codes

Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the are cocyclic. As a consequence, new class of that call full propelinear turns out. We prove their existence is equivalent to central relative (v, w, v, v/w)-difference sets. Moreover, some structural properties studied and examples provided. Some constructed for perform better than any comparable linear code.