My research interests include classical and quantum error-correcting codes, real and finite geometries, semifields and graphs and generally involve applying geometrical and linear algebra methods to these combinatorial objects.
I am currently supervising the following doctoral students, Tabriz Popatia and Robin Simoens (co-directing with Leo Storme). Ricard Vilar completed his doctorate under my supervision in March 2025.
I have published three books, the first entitled Finite Geometry and Combinatorial Applications, published in July 2015 by Cambridge University Press.
The second entitled A Course in Algebraic Error-Correcting Codes was published by Birkhauser in May 2020.
The third entitled A Course in Combinatorics and Graphs, was co-authored with Oriol Serra and was published by Birkhauser in April 2024.
There are videos of the course I gave on Coding and Information theory in the spring term of 2020 that more or less follows the content of the book.
There are also videos of the course I gave on Quantum Computation in the spring term of 2021.
I have set-up an Erratum page for the books. Please e-mail me if you find any errors or have any comments.
The following pdf files are edited from talks on
maximum distance separable codes: recent advances and applications (pdf), on sets defining few ordinary planes (pdf),
the maximum weight of a linear code (pdf), an alternative way to generalise the pentagon (pdf),
complete bipartite Turan numbers (pdf), the MDS conjecture for linear codes (pdf),
Jaeger's conjecture on nowhere zero points for linear maps (pdf), and functions over prime fields that do not determine all directions (pdf).
A proof of the MDS conjecture over prime fields (that linear maximum distance separable codes of dimension at most p have length at most p+1, where p is the number of elements in the field) is contained in this article. Here is a video of me trying to convince the participants of a BIRS (Banff International Research Station) workshop that it is a generalisation of Segre's ''arc is a conic'' theorem, the original proof of which is available here. Alternatively, here is another video of a similar talk, but with a more coding theory bias, from the 3rd International Castle Meeting on Coding Theory and Applications, held in Cardona in September 2011.
I have compiled a table of the maximum lengths of three-dimensional linear codes, where the difference between the length and minimum distance is fixed. There is also a short background on codes and (n,r) arcs and a question relating to the attainability of the Griesmer bound.
I am on the editorial board of Journal of Geometry, IEEE transactions on Information Theory and Journal of Combinatorial Theory, Series A.
There are notes available for the courses
An introduction to finite geometry in
pdf
format (65 pages),
co-authored with Zsuzsa Weiner.
This is the third edition updated September 2011.
Lacunary polynomials over finite fields in
dvi,
ps or
pdf
format (12 pages).
