Alain Couvreur
Published 2023-01-09Version 1
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.
Comments: Lecture notes for a course given at the Algebraic Coding Theory (ACT) summer school 2022
Remarks on codes from modular curves: MAGMA applications
Regular models of modular curves in prime level over ${\mathbb Z}_p^{\mathrm{ur}}$
Geometric realizations of representations for $\text{PSL}(2, \mathbb{F}_p)$ and Galois representations arising from defining ideals of modular curves
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