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Codes from Modular Curves

  • David Joyner
  • Jon-Lark Kim
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

One of the most interesting class of curves, from the perspective of arithmetical algebraic geometry, are the so-called modular curves. Some of the most remarkable applications of algebraic geometry to coding theory arise from these modular curves. It turns out these algebraic-geometric codes (“AG codes”) constructed from modular curves can have parameters which beat the Gilbert–Varshamov lower bound if the ground field is sufficiently large.

Keywords

Congruence Subgroup Modular Curve Rational Compactification Shimura Variety Modular Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentUS Naval AcademyAnnapolisUSA
  2. 2.Department of MathematicsUniversity of LouisvilleLouisvilleUSA

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