MAGMA Computational Algebra System

ALGEBRAIC-GEOMETRIC CODES

 
Acknowledgements
 
Introduction
 
Creation of an Algebraic Geometric Code
 
Properties of AG--Codes
 
Access Functions
 
Decoding AG Codes
 
Bibliography

DETAILS

 
Introduction

 
Creation of an Algebraic Geometric Code
      AlgebraicGeometricCode(S, D) : [PlcCrvElt], DivCrvElt -> Code
      AlgebraicGeometricDualCode(S, D) : [PlcCrvElt], DivCrvElt -> Code
      HermitianCode(q, r) : RngIntElt, RngIntElt -> Code
      Example CodeAlG_AlgebraicGeometricCode (H128E1)
      Example CodeAlG_AlgebraicGeometricCode (H128E2)

 
Properties of AG--Codes
      IsWeaklyAG(C) : Code -> BoolElt
      IsWeaklyAGDual(C) : Code -> BoolElt
      IsAlgebraicGeometric(C) : Code -> BoolElt
      IsStronglyAG(C) : Code -> BoolElt

 
Access Functions
      Curve(C) : Code -> Crv
      GeometricSupport(C) : Code -> DivCrvElt
      Divisor(C) : Code -> DivCrvElt
      GoppaDesignedDistance(C) : Code -> RngIntElt

 
Decoding AG Codes
      AGDecode(C, v, Fd) : CodeLinFld, ModTupFldElt, DivCrvElt -> ModTupFldElt

 
Bibliography

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