Codes and modular curves

01/09/2023

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by   Alain Couvreur, et al.

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These lecture notes have been written for a course at the Algebraic Coding Theory (ACT) summer school 2022 that took place in the university of Zurich. The objective of the course propose an in-depth presentation of the proof of one of the most striking results of coding theory: Tsfasman Vlăduţ Zink Theorem, which asserts that for some prime power q, there exist sequences of codes over 𝔽_q whose asymptotic parameters beat random codes.