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

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