Recent work in the development of diversity transformations for wireless systems has produced a theoretical framework for space-time block codes. Such codes are beneficial in that they may be easily concatenated with interleaved d trellis codes and yet still may be decoded separately. In this paper, a theoretical framework is provided for the generation of spatial block codes of arbitrary dimensionality through the use of orthonormal polynomial sets. While these codes cannot maximize theoretical diversity performance for given dimensionality, they still provide performance improvements over the single-antenna case. In particular, their application to closed-loop transmit diversity systems is proposed, as the bandwidth necessary for feedback using these types of codes is fixed regardless of the number of antennas used. Simulation data is provided demonstrating these types of codes′ performance under this implementation as compared not only to the single-antenna case but also to the two-antenna code derived from the Radon-Hurwitz construction.