Generalized Hadamard full propelinear codes

Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hadamard matrices are cocyclic. As a consequence, a new class of codes that we call generalized Hadamard full propelinear codes turns out. We prove that their existence is equivalent to the existence of central relative (v,w, v, v/w)-difference sets. Moreover, some structural properties of these codes are studied and examples are provided.Junta de Andalucía FQM-016Ministerio de Ciencia, Innovación y Universidades TIN2016-77918-