# Research

## Main research topics

### Finite Geometry and coding theory

My main area of expertise is finite geometry, in particular I study (substructures of) projective spaces and affine spaces over finite fields. Some topics: KM-arcs, optimal blocking multisets, quadrics, Hermitian varieties. You can click on each of those names for a short introduction to the topic.

I tend to look for linear algebra in geometric problems, which naturally leads to coding theory. A large part of my research also involves this link between coding theory and finite geometry: from geometrically constructed LDPC codes, over codes meeting the Griesmer bound, to linear codes defined by the incidence matrix of common geometric structures.

Recently, I started working on random network codes in the framework of this COST project and its links to cryptography.

A common misconception herein is that geometry only contributes to the more "applied" coding theory, and not vice versa. This is untrue: several of my best geometric results rely entirely on techniques from coding theory to produce they key observations leading to the results.

### Algorithmics

The other cornerstone of my research is algorithmic discrete mathematics. I have written libraries to work efficiently with various objects related to my research, such as finite fields, vector spaces, linear codes, projective spaces and their subspaces, quadrics, Hermitian varieties, etc. I can do most geometry that GAP can do, but often 10 - 10000 times faster.

I often assist other people's research with my computer results. Constructing the incidence matrix of PG(2,512), constructing all the generators of Q+(5,2), classifying small line sets with few odd-points in PG(2,7), generating the weight polynomial of a binary [525,50]-code, measuring LDPC performance, I have done all of them. Have a problem that you want solved much faster than GAP, or that is just too large for GAP? Or do you prefer to delegate any computer work to someone else? Send me an email, I'll be happy to take a look at it. And I love hard problems.

Fun fact: I have built a low-budget GPU supercomputer all by myself!