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arXiv · 1510.06425

One- and Two-Point Codes over Kummer Extensions

Ariane M. Masuda·Luciane Quoos·Alonso Sepúlveda
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Abstract

We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by $y^m=f(x)^λ$ 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.

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Ariane M. Masuda, Luciane Quoos, Alonso Sepúlveda. 2016-06-16. One- and Two-Point Codes over Kummer Extensions. https://doi.org/10.1109/tit.2016.2583437

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