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arXiv · 2106.13159

Weierstrass semigroup at $m+1$ rational points in maximal curves which cannot be covered by the Hermitian curve

Alonso Sepúlveda Castellanos·Maria Bras-Amorós
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Abstract

We determine the Weierstrass semigroup $H(P_\infty,P_1,\ldots,P_m)$ at several rational points on the maximal curves which cannot be covered by the Hermitian curve introduced by Tafazolian, Teher\'an-Herrera, and Torres. Furthermore, we present some conditions to find pure gaps. We use this semigroup to obtain AG codes with better relative parameters than comparable one-point AG codes arising from these curves.

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Alonso Sepúlveda Castellanos, Maria Bras-Amorós. 2021-06-24. Weierstrass semigroup at $m+1$ rational points in maximal curves which cannot be covered by the Hermitian curve. https://doi.org/10.1007/s10623-020-00757-4

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