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

Giovanni Falcone; Giuseppe Filippone

doi:10.1007/s12095-024-00713-2

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arXiv · 2303.08441

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

Giovanni Falcone·Giuseppe Filippone

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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.

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Giovanni Falcone, Giuseppe Filippone. 2023-03-15. Mumford representation and Riemann Roch space of a divisor on a hyperelliptic curve. https://doi.org/10.1007/s12095-024-00713-2

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