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.
CITATION STYLE
Joyner, D., & Kim, J. L. (2011). Codes from modular curves. In Applied and Numerical Harmonic Analysis (pp. 145–176). Springer International Publishing. https://doi.org/10.1007/978-0-8176-8256-9_6
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