Research
My research focusses on substructures of finite projective spaces and finite classical polar spaces, including links with coding theory. In particular, I perform research on caps, arcs, blocking sets, minihypers, partial spreads and covers of finite classical polar spaces.Related topics in coding theory include the problem of finding and characterizing linear codes meeting the Griesmer bound, LDPC codes associated to geometrical structures, and the linear codes associated to the Desarguesian projective spaces.
Typical problems are to find characterizations and classifications of these substructures, e.g. what is the smallest blocking set of a particular polar space? We also want to investigate typical properties: how many points does such a blocking set contain? What is the geometrical structure?
Publications
PublicationsSurvey article on substructures of finite projective spaces
In the articles:
- J.W.P. Hirschfeld and L. Storme, The packing problem in statistics, coding theory, and finite projective spaces, Proceedings of the Bose Memorial Conference (Colorado, June 7-11, 1995). J. Statist. Planning Infer. 72 (1998), 355-380.
- J.W.P. Hirschfeld and L. Storme, The packing problem in
statistics, coding theory and finite projective spaces: update 2001. Developments in Mathematics Vol. 3,
Kluwer Academic Publishers. Finite Geometries,
Proceedings of the Fourth Isle of Thorns Conference (Chelwood Gate, July 16-21,
2000) (Eds. A. Blokhuis, J.W.P. Hirschfeld, D. Jungnickel and J.A. Thas), pp. 201-246.
survey_article Fourth Isle of Thorns Conference .
a survey of results on arcs, caps, (multiple) blocking sets, (k,n)-arcs, and minihypers is presented. The first article contains the main results up to 1995, the second article all main results up to 2001.
Prof. Hirschfeld and I would like to keep these articles up-to-date.
For this reason, we invite all who improves a result in one of the tables to mail that result to J.W.P. Hirschfeld (jwph@sussex.ac.uk) and to L. Storme (leo.storme@ugent.be). (important: the old email address ls@cage.ugent.be does not work anymore)
Thank you in advance!
Editor
I am an editor of the following international mathematical journals.- Finite Fields and Their Applications
- Innovations in Incidence Geometry
- Journal of Combinatorial Designs
- Serdica Mathematical Journal