Codes and modular curves

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 Vl\u{a}du\c...

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Bibliographic Details
Main Author Couvreur, Alain
Format Journal Article
LanguageEnglish
Published 09.01.2023
Subjects
Computer Science - Information Theory
Mathematics - Algebraic Geometry
Mathematics - Information Theory
Mathematics - Number Theory
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Summary: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 Vl\u{a}du\c{t} Zink Theorem, which asserts that for some prime power $q$, there exist sequences of codes over $\mathbb{F}_q$ whose asymptotic parameters beat random codes.
DOI:10.48550/arxiv.2301.03569