Many of the problems studied concern fundamental mathematical structures and their properties and are often motivated by applications in ICT.
The origin of the work can be traced back to a thesis from the early 1990s. The early work on combinatorial and computer-aided construction methods for covering codes was later extended to general coding theory, design theory, graph theory, Shannon theory, and combinatorial algorithms, that is, it is now touching large parts of discrete mathematics and information theory.
The questions studied are commonly about:
- existence – do certain structures exist?
- counting – how many are there?
- classification –what do they look like, up to symmetry?
Computational methods are becoming state-of-the-art within many research fields.
One example of a result achieved by the group, and which made the work known to a wider audience, is the classification of the 11084874829 Steiner triple systems of order 19. More recent results are the discovery of a q-analog of a Steiner triple system of order 13 and a study showing nonexistence of a McLaughlin geometry. The former result, obtained in joint work with researchers from Germany, Israel and the United States, drew international attention.
Massive computations require massive computational resources. The team is a regular user of computational resources made available by the department, the school, the university, and others including CSC. Since 2010, the team has PC clusters of its own, hydra (a many-headed serpent in Greek mythology) and medusa (a monster described as having the face of a woman with snakes in place of hair), with a total of more than 700 cores.
We are happy to enjoy the time before price of electricity surpasses price of equipment as the major cost issue.
The work of the research group is supported in part by the Academy of Finland under project #289002: Construction and Classification of Discrete Mathematical Structures.
The research group is led by Professor Patric Östergård.