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The parameters of duals of algebraic geometric codes on surfaces


Speaker: Dr. Alain Couvreur , INRIA.

abstract

It is well-known in the theory of codes on curves that the dual of an algebraic-geometric code on a curve is an algebraic-geometric code on the same curve. It turns out that this property does not hold in general when the curve is replaced by an higher dimensional variety. This observation motivates the study of this new class of codes which are the duals of algebraic geometric codes on higher-dimensional varieties.

In this talk, after a brief review on the classical properties of codes on curves, we will focus on the problem of finding the parameters of duals of codes on surfaces. A method yielding a lower bound for the minimum distance of such codes will be presented. This method, based on the use of differential 2-forms and intersection theory on surfaces, turns to be efficient provided the Picard Number of the surface is small.