Outcomes

This project deals with construction and analysis of various types of combinatorial designs and graphs. For construction of combinatorial structures we will combine computational, geometric and algebraic approach. We will also take into consideration other combinatorial objects, such as binary complementary sequences (e.g. periodic Golay pairs) and Hadamard matrices (including complex Hadamard matrices). Relations to other structures (finite geometries, association schemes, etc.) will also be taken into account. Finite groups actions will have a significant role in constructing and analysing combinatorial structures. Further, we will work on construction and analysis of codes, mostly linear codes that can be obtained from combinatorial designs, graphs, binary sequences and Hadamard matrices. As a result of the proposed research, we expect a construction and classification of various types of combinatorial designs and graphs (e.g. new block designs and strongly/distance regular graphs) and other combinatorial objects (complementary sequences, Hadamard matrices, etc.), as well as a construction of codes with good properties (e.g. linear codes with large minimum distance comparing to the length and the dimension of the code, self-dual codes, etc.). We expect that the outcomes of this project will be of interest for researchers working in design theory, coding theory and graph theory, and for those working in theory of finite groups.