Properties of AG–Codes

IsWeaklyAG(C): Code -> BoolElt

Return true if and only if the code \(C\) is a weakly algebraic–geometric code, i.e. \(C\) has been constructed as an algebraic–geometric code with respect to a divisor of any degree.

IsWeaklyAGDual(C): Code -> BoolElt

Return true if and only if the code \(C\) was constructed as the dual of a weakly algebraic–geometric code.

IsAlgebraicGeometric(C): Code -> BoolElt

Return true if and only if the code \(C\) is of algebraic–geometric construction of length \(n\), built from a divisor \(D\) with \(deg(D) < n\).

IsStronglyAG(C): Code -> BoolElt

Return true if and only if \(C\) is an algebraic–geometric code of length \(n\) constructed from a divisor \(D\) satisfying \(2g-2 < deg(D) < n\), where \(g\) is the genus of the curve.