Optimal codes on vector combinatorial configurations
Journal Title: Vìsnik Nacìonalʹnogo unìversitetu "Lʹvìvsʹka polìtehnìka". Serìâ Ìnformacìjnì sistemi ta merežì - Year 2015, Vol 814, Issue
Abstract
Concept of coding systems optimizations based on vector combinatorial configurations (the Ideal Vector Rings models), with the optimization being embedded in the underlying combinatorial models, is regarded in this paper. This paper is aimed at improving the qualitative indices of multidimensional vector data information technologies and computer systems with respect to transmission speed of vector data with automatic error correction, and data security using a variety of multidimensional combinatorial configuration and finite cyclic group theory. Some problems of computer engineering and information technologies which deal with profitable use of mathematical methods for optimization of coding systems based on the two-and multidimensional Ideal Ring Bundles (tD-IRB)s are regarded with special attention being paid to interpretations of multidimensional Ideal Ring Bundles as vector cyclic groups and its numerous isomorphic transformations using theoretical relation of the mathematical models with reference to the well-known cyclic difference sets theory. The possibility for design of high performance systems of the optimal monolithic vector coding systems which provide vector data coding in torus frame of reference using combinatorial optimization is shown. It is proved that the proposed techniques provide design of high performance vector data coding and control systems using combinatorial optimization. Definitions of the Ring Monolithic Vector Codes are given such as Numerical Optimum Ring Code, Two-dimensional Optimum Ring Code and Multidimensional Optimum Ring Code. These design techniques make it possible to configure optimal two- and multidimensional vector coding systems using fewer code combinations in the system, while maintaining or improving on code size and the other significant operating characteristics using high speed corrected coding possibility of the system.
Authors and Affiliations
Volodymyr Riznyk
Keywords
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