Algebraic Geometric codes from Kummer Extensions
  For Kummer extensions defined by $y^m = f (x)$, where $f (x)$ is a separable polynomial over the finite field $\mathbb{F}_q$, 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 many points algebraic geometric codes with good parameters. 
Daniele Bartoli, Luciane Quoos, Giovanni Zini
math.AG cs.IT math.IT