  We compute the Weierstrass semigroup at one totally ramified place for Kummer
extensions defined by $y^m=f(x)^{\lambda}$ where $f(x)$ is a separable
polynomial over $\mathbb{F}_q$. In addition, we compute the Weierstrass
semigroup at two certain totally ramified places. We then apply our results to
construct one- and two-point algebraic geometric codes with good parameters.
