How arithmetic and geometry make error correcting codes better

10/21/2021

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by   Alain Couvreur, et al.

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This note completes a talk given at the conference Curves over Finite Fields: past, present and future celebrating the publication the book Rational Points on Curves over Finite Fields by J.-P. Serre and organised at Centro de ciencias de Benasque in june 2021. It discusses a part of the history of algebraic geometry codes together with some of their recent applications. A particular focus is done on the "multiplicative" structure of these codes, i.e. their behaviour with respect to the component wise product. Some open questions are raised and discussed.