Mumford representation and Riemann Roch space of a divisor on a hyperelliptic curve

03/15/2023

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by   Giovanni Falcone, et al.

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For an (imaginary) hyperelliptic curve ℋ of genus g, with a Weierstrass point Ω, taken as the point at infinity, we determine a basis of the Riemann-Roch space ℒ(Δ + m Ω), where Δ is of degree zero, directly from the Mumford representation of Δ. This provides in turn a generating matrix of a Goppa code.