Multi-dimensional systems based on perfect combinatorial models

Abstract

The paper is concerned with the innovative techniques of multidimensional systems design based on multidimensional combinatorial sequencing theory, namely the concept of gold ring bundles (GRB), which can be used for finding optimal solutions for wide classes of technological problems. Research into the underlying mathematical principles relating to the optimal placement of structural elements in spatially/temporally distributed multi-dimensional systems with non-uniform structure (e.g. two-dimensional arrays of radio antennas) or to the optimal choice of parameters in multi-dimensional systems (e.g. vector data coding systems, vector distributed electrical circuits, vectorisation systems etc.). These design techniques make it possible to configure multi-dimensional systems with fewer components then at present, while maintaining or improving on resolving ability, high-speed operation, and the other significant operating characteristic of the system. In particular, these results have been developed for the synthesis of nonuniformly spaced thinned antenna arrays with low level of side lobes. The results, essentially, relate to the development of new algebraic constructions based on the idea of perfect combinatorial configurations, such as cyclic difference sets, due to the remarkable properties and structural perfection of GRBs provide an ability to reproduce the maximum number of combinatorial varieties in the system with a limited number of elements and bonds. (4 pages)