Abstract
This paper involves techniques for improving the quality indices of big data process engineering with respect to high-performance coded design, transmission speed, and reliability under manifold coordinate systems. The system formed with limited number of basis vectors. The set of modular sums of the vectors including themselves form t-dimensional toroidal coordinate grid over the toroid, and the basis is sub-set of general number of grid coordinate set. These design techniques make it possible to configure high performance information technology for big data coding design and vector signal processing. The underlying mathematical principles relate to the optimal placement of structural elements in spatially or temporally distributed systems by the appropriate algebraic constructions based on cyclic groups in extensions of Galois fields, and development of the scientific basis for optimal solutions for wide classes of technological problems in big data process engineering and computer science.
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