Kozhukhovska O. Models and methods of orthogonal discrete changes of Walsh and their usage in the systems of open encoding

The object of the investigation - improvement processes of the systems of open coding. The subject of investigation - models and methods of orthogonal discrete changes of Walsh and Fourier and their usage in coding of information on the base of Reed- Muller's codes for systems of open coding. Methods of investigation are based on the usage of matrix algebra, math ematical means of cronekers multiplication of matrix, elements of theory of digital processing of signal coding, vectorization of quick changes of Walsh and Fourier. There have been developed models and methods of cronekers multiplication of matrix and examined their features that helped to use them for paralleling and vectorization of matrix of orthogonal discrete changes and improve time indicator of calculation. On the base of cronekers multiplication of matrix there have been improved methods of paralleling and vectorization of Fourier and Walsh matrix that allowed to use them for the real time and in vector regime and reduce the volume of necessary memory for a computer system. There has been developed a method of transition from Walsh function basis to Fourier function basis that allowed getting algorithms of quick changes of Fourier and Walsh without shift of the initial data in the form of the law of binary inversion and returning code of Grey. There has been improved the organization of vector calculation of algorithms of quick changes of Fourier and Walsh that allowed to conduct analysis of vector algorithms of specified changes with the help of algorithms of splitting and Gentlemen- Sende. There has been modified a range of methods of coding and decoding of Reed - Muller's codes of first range using quick changes of Walsh-Adamar and Walsh -Pelly that allowed to implement them in the regime of real time and in vector regime for computer with the command architecture "one command, multiple data" on the base of models of orthogonal discrete changes for the task of Reed-Muller's coding in the system of open coding. There have been got results implemented in industry and study process of Cherkassy Technological University.