This paper involves a new conceptual methodology for improving the quality indices of vector information technologies (e.g. vector data coding) with respect to performance reliability, transmission speed, and functionality, using novel designs based on vector combinatorial configurations such as cyclic groups in extensions of Galois fields, difference sets and novel vector combinatorial constructions. Research into combinatorial structures of two- and higher dimensionality makes it possible to configure vector information systems based on the idea of an optimal placement of structural elements in the systems. These design techniques allow information to be presented, processed, transfered, and transmited as two- or multidimensional vector data flows with fewer base elementsю. The aim is to imploy the appropriate algebraic techniques to improve the technological efficiency making use of the applicable properties of interconnections of two- and multi-modular vector cyclic groups, and inter-convertible dimensionality of the vector information systems. The paper contains some examples of the minimization related to the optimal placement of structural elements in a spatially or temporarily distributed information system, including its application to the design of coded signals for communications and radar, and positioning the elements in antenna arrays.
- M. Hall, Combinatorial Theory. Waltham, MA, USA: Blaisdell Publishing Company, 1967.
- J. Rotman, Galois Theory, 2nd ed. Berlin, Germany: Springer, 1998.
- T. Cormen, C. Leiserson, R. Rivest, and C. Stein,Introduction to Algorithms, 2nd ed. The MIT Press and McGraw-Hill Book Company, 2001.
- N. Bourbaki, Algebra II. Berlin, Germany: Springer, 2003.
- M. Greenberg, Lectures on Forms in Many Variables. New York-Amsterdam: W.A. Benjamin, Inc, 1969.
- A. Fröhlich and M. Taylor, Algebraic number theory (Cambridge studies in advanced mathematics. 27). Cambridge, UK: Cambridge University Press, 1991.
- P. McMullen and E. Schulte, Abstract Regular Polytopes. Cambridge, UK: Cambridge University Press, 2002.
- Manifold, https://en.wikipedia.org/wiki/Manifold
- Yu. Shapovalov, B.Mandziy, and D. Bachyk, “Optimization of linear parametric circuits in the frequency domain”, Econtechmod: an international quarterly journal on economics in technology, new technologies and modelling processes, vol. 4, no. 2, pp. 73-77, 2013.
- A.Holovatyy, V.Teslyuk, and M.Lobur, “Verilog-ams model of comb-drive sensing element of integrated capacitive microaccelerometer for behavioural level of computer aid design”, Econtechmod: an international quarterly journal on economics in technology, new technologies and modelling processes, vol. 3, no.1, pp. 49-53, 2014.
- V.V. Riznyk, Synthesis of the optimum combinatorial systems, Lviv, Ukraine: Vyshcha shkola, 1989. (Ukrainian)
- V.Riznyk “Applications of the combinatorial configurations for optimization of technological systems”, Econtechmod: an international quarterly journal on economics in technology, new technologies and modelling processes, vol. 5, no.1, pp. 52-57, 2016.