How arithmetic and geometry make error correcting codes better
Algebraic Geometry
2022-04-05 v2 Information Theory
math.IT
Number Theory
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.
Keywords
Cite
@article{arxiv.2110.11282,
title = {How arithmetic and geometry make error correcting codes better},
author = {Alain Couvreur},
journal= {arXiv preprint arXiv:2110.11282},
year = {2022}
}