  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 $n=4.$
