Remarks on codes from modular curves: MAGMA applications

Abstract

Expository paper discussing AG or Goppa codes arising from curves, first from an abstract general perspective then turning to concrete examples associated to modular curves. We will try to explain these extremely technical ideas using a special case at a level to a typical graduate student with some background in modular forms, number theory, group theory, and algebraic geometry. Many examples using MAGMA are included.

29 pages

References in corpus (2)

• Commutators, Lefschetz fibrations and the signatures of surface bundles
• Computing the Automorphism Groups of Hyperelliptic Function Fields

Cited by in corpus (7)

• Calabi-Yau Caps, Uniruled Caps and Symplectic Fillings
• Positive factorizations of mapping classes
• Lefschetz pencils and finitely presented groups
• New Exotic 4-Manifolds via Luttinger Surgery on Lefschetz Fibrations
• Spin Lefschetz fibrations are abundant
• Classification of genus-$1$ holomorphic Lefschetz pencils
• Proportion of cyclic matrices in maximal reducible matrix algebras