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How arithmetic and geometry make error correcting codes better

Alain Couvreur 1 
1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : 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.
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Contributor : Alain Couvreur Connect in order to contact the contributor
Submitted on : Monday, October 25, 2021 - 10:40:52 AM
Last modification on : Thursday, January 20, 2022 - 4:13:46 PM

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  • HAL Id : hal-03400779, version 1
  • ARXIV : 2110.11282


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



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