My main fields of research include

algebraic and combinatorial coding
(notably, in Hamming space, problems related to the covering radius of codes, binary or nonbinary,
and the construction of perfect codes with the Hamming parameters;
or the topic of codes identifying --- in a broad meaning --- vertices in graphs, see, e.g.,
the hexagonal mesh below. This contains identifying codes, locating-dominating codes,
discriminating codes, as well as new concepts such as adaptive identification and watching systems,
and is my main topic now [2008]);

for arithmetic codes, the study of metrics, leading
to the construction of perfect codes
or to results of nonexistence;

complexity,
applied to problems in coding, graph theory or cryptography
(e.g., calculating the minimum distance or the norm of a code,
existence of identifying codes of given size, containing a given subset,
fast modular exponentiation, ...).