Models of optimum discrete signals on the ring combinatorial configurations

Abstract

The innovative techniques for improving the quality indices of radio-signals for communications and radars with non-uniform structure (e.g. code sequences) with respect to error protection, using novel combinatorial configurations such as cyclic difference sets and Ideal Ring Bundles (IRB)s was regarded. Method for construction of optimum discrete signals, based on these models is proposed. IRBs are cyclic sequences of positive integers, which form perfect partitions of a finite interval [1,N]. The sums of connected sub-sequences of an IRB enumerate the set of integers [1,N-1] exactly R-times. This property makes IRBs useful in applications, which need to partition sets with the smallest possible number of intersections. The models of optimum discrete signals, having previously unknown favorable property, which hold for the same set of the IRBs in varieties permutations of its terms, named the "Glory to Ukraine Stars” have been indicated as a cluster of combinatorial configurations. Some algorithms and useful examples for constructing of optimum cyclic error-correcting codes presented. It shows that remarkable properties of IRBs have encoded in fine structure of circular symmetry and asymmetry ensembles. There are great classes of new two- and multidimensional IRBs, which being in excess classic models of optimum discrete signals with respect to number and combinatorial varieties. Indicate that the IRBs to be in exceed of classic perfect difference sets multiply.