Departament de Matemàtiques
Universitat Politècnica de Catalunya
Escola d'Enginyeria de Telecomunicacio i Aerospacial de Castelldefels
Campus de Baix Llobregat
Avinguda del Canal Olimpic, 15
Tel: +34.93.413.41.03 / Fax: +34.93.401.59.81
An HTML version of my Curriculum
Vitae is available. It is possible to view articles from the
list of publications.
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 have published two books, one entitled Finite Geometry and Combinatorial Applications, published in July 2015 by Cambridge University Press.
The other entitled A Course in Algebraic Error-Correcting Codes was published by Birkhauser in May 2020.
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.
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.
A quote from Lockhart's Lament "The mathematics curriculum doesn't need to be reformed, it needs to be scrapped". Read it to find out what it should be replaced by.
There are notes available for the courses
An introduction to finite geometry in
format (65 pages),
co-authored with Zsuzsa Weiner.
This is the third edition updated September 2011.
Lacunary polynomials over finite fields in
format (12 pages).
Updated May 2020