Multidimensional signals and cyclic codes over torus geometry

This paper generalizes the duality between multidimensional cyclic codes and torus groups. Innovative multidimensional coded design techniques for improving the quality indices of data coding (e.g. self-checking codes) based on tori geometry, is given. These design techniques make it possible to configure high performance multidimensional coded systems and design of signals for communications and radar with respect to redundancy, signal reconstruction, security, and low side lobe antenna design.