  We determine the Weierstrass semigroup $H(P_{\infty}, P_{1}, \ldots , P_{m})$
at several points on the $GK$ curve. In addition, we present conditions to find
pure gaps on the set of gaps $G(P_{\infty}, P_{1}, \ldots , P_{m})$. Finally,
we apply the results to obtain AG codes with good relative parameters.
