Outcomes

The project will mainly conduct research in the field of algebraic design theory, algebraic graph theory, and the study of codes, especially in the field of algebraic coding theory. In the field of design theory, the project will deal, among other things, with the construction of combinatorial designs from finite groups. Such research, in addition to contributing to design theory, also contributes to a better understanding of finite groups. In particular, we will study the designs on which finite simple groups act, since the study of the finite simple groups is of crucial importance in group theory. Designs will be constructed in other ways as well, e.g. using linear codes and heuristic methods. Hadamard matrices, which are closely related to combinatorial designs, will also be studied. Hadamard matrices have numerous applications, for example in physics, coding theory, signal processing and spectrometry, which gives additional importance to their study. In the study of graphs and directed graphs, special attention will be paid to regular graphs, e.g. strongly regular and other distance-regular graphs and quasi-strongly regular graphs and digraphs. Association schemes, which are closely related to distance-regular graphs, will also be studied. The study of distance regular graphs and association schemes is a central part of algebraic graph theory. When studying graphs and digraphs, special attention will be paid to their automorphism groups. In particular, graphs on which finite simple groups act will be studied. In the course of research in coding theory, various types of linear codes over fields and rings will be studied, as well as codes defined on graphs that have transitive and neighbour-transitive groups of automorphisms. The connection between codes and combinatorial designs, graphs and association schemes will be studied. Further, q-analogues of designs and graphs, their automorphism groups and associated subspace codes will be studied.