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Magma
Computer • algebra
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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 (H162E1)
Example
CodeAlG_AlgebraicGeometricCode (H162E2)
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
Example
CodeAlG_AGDecode (H162E3)
Toric Codes
ToricCode(P, q) : TorPol, RngIntElt -> Code
ToricCode(S, q) : SeqEnum[TorLatElt], RngIntElt -> Code
Example
CodeAlG_ToricCode (H162E4)
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V2.28, 28 February 2025