Département d'ingénierie informatique

This research is concerned with the combinatorial and algebraic framework that is most naturally adapted to the study of error-correcting codes and some generalizations. It deals mainly with the subject of \emph{association schemes}, which is related to graph theory, group theory, and orthogonal polynomials.

Questions of major interest include:

• to obtain upper bounds on the size of a code with a given distance and lower bounds on the size of a design with a given strength,
• to investigate the formal duality that links the code and design concepts,
• to discover the combinatorial significance of a design in a given association scheme.

1. Association schemes and coding theory, P. Delsarte and V.I. Levenshtein, IEEE Trans. Inform. Theory, vol. 44, 1998, pp. 2477-2504.
2. Beyond the orthogonal array concept, P. Delsarte, European J. Combinatorics (to appear)