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arXiv · 1803.03518

Subcovers and codes on the $X_{n,r}$ curves

Herivelto Borges·Alonso S. Castellanos·Guilherme Tizziotti
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Abstract

In this work, subcovers $\mathcal{X}_{n,r}^s$ of the curve $\mathcal{X}_{n,r}$ are constructed, the Weierstrass semigroup $H(P_\infty)$ at the point $P_\infty \in \mathcal{X}_{n,r}^s$ is determined and the corresponding one-point AG codes are investigated. Codes establishing new records on the parameters with respect to the previously known ones are discovered, and $108$ improvements on MinT tables are obtained.

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Herivelto Borges, Alonso S. Castellanos, Guilherme Tizziotti. 2018-03-09. Subcovers and codes on the $X_{n,r}$ curves. https://arxiv.org/abs/1803.03518

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