Phase-rotational invariance properties for two-level constructed, (usi
ng a binary code and a code over a residue class integer ring as compo
nent codes) Euclidean space codes (signal sets) in two and four dimens
ions are discussed. The label codes are group codes over dihedral and
dicyclic groups respectively. A set of necessary and sufficient condit
ions on the component codes is obtained for the resulting signal sets
to be rotationally invariant to several phase angles.