Optimization of Encoding Design Based on the Spatial Geometry Remarkable Properties

Abstract

This paper involves techniques for optimization of encoding design based on the remarkable geometric property of ring symmetry which contains two complementary asymmetries as the World harmony law for improving the quality indices of one- and multidimensional cyclic codes with respect to performance reliability, transmission speed, and transmission content, using vector data coding. These design techniques make it possible to configure encoding system with minimized number of digit weights, while maintaining or improving on error protection, security, and function of autocorrelation. Such sets are t-dimensional vectors, each of them together with all their modular sums enumerate the set node points grid of the coordinate system with the corresponding sizes and dimensionality. Systemic researches based on remarkable geometric properties of multi-modular mathematical structures such as “Glory to Ukraine Star” (GUS) combinatorial configurations demonstrated.