Application of Drinfeld modular curves in Coding Theory
Organizers
Speaker
Time
Wednesday, October 25, 2023 12:00 PM - 1:00 PM
Venue
A4-1
Abstract
By Goppa's construction, good towers yield good linear error-correcting codes. The existence of long linear codes with the relative good parameters above the well-known Gilbert-Varshamov bound discovery by Tsfasman et al, provided a vital link between Ihara's quantity and the realm of coding theory.
Good towers that are recursive play important roles in the studies of Ihara's quantity, usually constructed from modules curves. Elkies deduced explicit equations of rank-2 Drinfeld modular curves which coincide with the asymptotically optimal towers of curves constructed by Garcia and Stichtenoth. In 2015, Bassa, Beelen, Garcia, and Stichtenoth constructed a celebrated (recursive and good) tower (BBGS-tower for short) of curves and outlined a modular interpretation of the defining equations. Soon after that, Gekeler studied in depth the modular curves coming from sparse Drinfeld modules. In this talk, to establish a link between these existing results, I propose a generalized Elkies' Theorem which tells in detail how to directly describe a modular interpretation of the equations of the BBGS tower.
Speaker Intro
Hu chuangqiang joined Bimsa in the autumn of 2021. The main research fields include: coding theory, function field and number theory, singularity theory. In recent years, he has made a series of academic achievements in the research of quantum codes, algebraic geometric codes, Drinfeld modules, elliptic singular points, Yau Lie algebras and other studies. He has published 13 papers in famous academic journals such as IEEE Trans. on IT., Final Fields and their Applications, Designs, Codes and Cryptography. He has been invited to attend domestic and international academic conferences for many times and made conference reports.