Recently reported multidimensional geometrically uniform signal constellations (L x MPSK and Decomposed-Lattice constellations) are joined in the term of Generalized Permutation Alphabets (GPA). Possibility of a binary isometric labeling of GPA's is completely characterized. An algorithm for constructing generating groups of PSK-type GPA is proposed. We show that this concept, when is extended to the lattice, gives rise to a class of new coset codes which perform out best codes listed in [11].