Models of optimum multidimensional signals on the vector combinatorial configurations

Abstract

New conceptual models for construction of optimum multidimensional discrete signals as binary monolithic code in which any allowed code word consists no more than one solid row of the same symbols in the ring topology sequence, named an ``Optimum Monolithic Ring'' code (OMR-code) are considered. All code combinations of an OMR-code enumerate the set of t-coordinates specified with respect to t-dimensional cyclic frame reference exactly R-times. The remarkable technical merits of ``Glory to Ukraine Star'' configuration, which properties hold for the same set of an OMR-code in varieties permutations of its terms is demonstrated, and method for design of two- or multidimensional vector signals coded based on the optimum binary monolithic code is presented. Proposed vector models of discrete signal optimization provide, essentially, a new approach to generalize them to great class of optimized problems in radio-telecommunications, navigation and information technology. Moreover, the optimization is embedded in the underlying combinatorial models. The favourable qualities of the Optimum Multidimensional Ring code provide breakthrough opportunities to apply them to numerous branches of science and advanced technology, with direct applications to vector data telecommunications, vector encoded design, and optimal vector information technology.