Applications of finite geometry in spectral graph theory and in classical and quantum error-correction

01 November 2023 → 31 October 2027
Research Foundation - Flanders (FWO)
Research disciplines
  • Natural sciences
    • Linear and multilinear algebra, matrix theory
    • Geometry
    • Combinatorics
    • Coding and information theory
    • Quantum information, computation and communication
Finite geometry Coding theory Spectral graph theory
Project description

The proposed project consists of three topics that are linked by finite geometry and by the techniques that are used to investigate them. They are situated in modern research areas with many applications and are of current international interest. We devote a work package (WP) to each topic. WP1 (Finite geometry and spectral graph theory) focuses on determining the cospectrality of graphs coming from finite geometries, thus giving new insights in the spectral graph characterization problem. We will provide new classes of strongly regular graphs and interesting graphs for quantum information theory. WP2 (Finite geometry and classical error-correction) investigates bounds on the parameters of sets of projective subspaces, which can be used for Random Network Coding. We will also look for constructions and parameters of codes defined by incidence geometries. WP3 (Finite geometry and quantum error-correction) translates existing quantum error-correcting codes into geometrical structures to provide more insight into making these codes more efficient. The interaction between the topics is still growing, as new links have been discovered only recently. The topics are being studied thoroughly, but little has been done on the intermediate correspondence of the topics, making this project original. It is realistic that more links can be established, which has already proven to be fruitful in the past.