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.

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