  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.
