Алгебрични, геометрични и комбинаторни методи в теория на кодирането

The coding theory is developed in Bulgaria already over 50 years as the beginning was set by acad. Stefan Dodunekov (1945-2012). The Bulgarian school has constantly stood on top or ahead of the curve, exploring new and emerging topics and applications in the field with the clear vision that the development and refinement of innovative research methods is crucial for the achievement of new knowledge.

The present project proposal is directed to fundamental research in the field which is based on algebraic, geometric and combinatorial methods, applied separately and together. Because of its timeliness and importance for data protection nowadays the Coding theory is developing in many basic for the electronic communications and informatics directions, in whose foundations structures with interesting algebraic, geometric and combinatorial properties are laid. Such structures are the spherical codes and designs, codes and orthogonal arrays in Hamming spaces, maximal codes and minimal designs in different polynomial metric spaces, projective geometries and their substructures, combinatorial designs and graphs with certain properties, all these considered in the project.

The team of the project has long research experience in the investigation of such objects. The used methods concern obtaining bounds for important parameters of combinatorial structures as well as derivation of constructions and classification results. The methods used are heavily based on mathematics (algebra, geometry, numerical analysis, combinatorics, graph theory, etc.), but for investigation of new ideas and obtaining good results fast and efficient algorithms related to development of complex software are also needed. This implies synchronisation and efficiency of the team in the research.

The scientific team includes not only researchers with experience in the field but also young researchers just starting or developing their scientific career, who will obtain a lot of new knowledge and bring fresh ideas to the work.