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Mumford representation and Riemann Roch space of a divisor on a hyperelliptic curve (2303.08441v1)
Published 15 Mar 2023 in math.AG, cs.IT, and math.IT
Abstract: For an (imaginary) hyperelliptic curve $ \mathcal{H} $ of genus $g$, with a Weierstrass point $\Omega$, taken as the point at infinity, we determine a basis of the Riemann-Roch space $\mathcal{L}(\Delta + m \Omega)$, where $\Delta$ is of degree zero, directly from the Mumford representation of $\Delta$. This provides in turn a generating matrix of a Goppa code.