How arithmetic and geometry make error correcting codes better

Alain Couvreur (1)

1 GRACE - Geometry, arithmetic, algorithms, codes and encryption

This note completes a talk given at the conference Curves over Finite Fields: past, present and future celebrating the publication the book {\em 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.

Domaines: Géométrie algébrique [math.AG]; Théorie de l'information [cs.IT]; Théorie des nombres [math.NT]

Alain Couvreur. How arithmetic and geometry make error correcting codes better. 2021. ⟨hal-03400779⟩