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

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.

8 pages