NIR 2.2200.2017 / 4.6 "Search and study of extremal quasi-orthogonal matrices for information processing problems"

As part of the research work, methods for the synthesis of low-level quasi-orthogonal matrices for image processing tasks that meet the needs of today are proposed and investigated. Matrices have different orders and structures, including symmetric, cyclic, block-cyclic, etc., economical for storage and generation, which provides algorithm developers with ample opportunities to choose the most suitable ones.  

   Features of some of the considered matrices (Mersenne and Raghavarao) make it possible, on their basis, to obtain new code sequences, nested codes for the formation of marked code-modulated signals in modern telecommunication data transmission systems based on the set of IEEE 802.11 standards, as well as in modern multi-position radar systems.
    The considered codes, according to their autocorrelation functions obtained in the work and the ratio of the peak of the autocorrelation function to the maximum sidelobe in absolute value, are an alternative to the well-known Barker codes of length 3, 4, 5, 7, 11, 13. Separately, the characteristics of nested codes, which are a combination of Barker codes , Mersenne and Raghavarao.