Algebraic geometric codes on many points from Kummer extensions

For Kummer extensions defined by ym=f(x), where f(x) is a separable polynomial over the finite field Fq, we compute the number of Weierstrass gaps at two totally ramified places. For many totally ramified places we give a criterion to find pure gaps at these points and present families of pure gaps. We then apply our results to construct n-points algebraic geometric codes with good parameters.