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arXiv · 2012.08870

Explicit bases of the Riemann-Roch spaces on divisors on hyperelliptic curves

Giovanni Falcone·Ágota Figula·Carolin Hannusch
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Abstract

For an (imaginary) hyperelliptic curve $\mathcal{H}$ of genus $g$, we determine a basis of the Riemann-Roch space $\mathcal{L}(D)$, where $D$ is a divisor with positive degree $n$, linearly equivalent to $P_1+\cdots+ P_j+(n-j)\Omega$, with $0 \le j \le g$, where $\Omega$ is a Weierstrass point, taken as the point at infinity. As an application, we determine a generator matrix of a Goppa code for $j=g=3$ and $n=4.$

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Giovanni Falcone, Ágota Figula, Carolin Hannusch. 2020-12-16. Explicit bases of the Riemann-Roch spaces on divisors on hyperelliptic curves. https://arxiv.org/abs/2012.08870

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