  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.
