Multi-modular Optimum Coding Systems Based on Remarkable Geometric Properties of Space

In this paper, we regard a new conceptual model of multi-modular optimum coding systems as multi-modular cyclic groups based on remarkable geometric properties of space, namely useful rotational symmetry and asymmetry relationships law. Moreover, the optimization embedded in the models. Proposed methodology provides the development of new directions in fundamental and applied research in systems engineering for improving the quality indices of engineering devices or systems (e.g. 3D space coordinates control system) with respect to redundancy, and embody reliability. These design techniques make it possible to configure systems with fewer elements than at present, while maintaining or improving on resolving ability, structural redundancy and security of the system. Examples of optimum vector codes over multimodular toroidal coordinate systems presented.