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

06/24/2021

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by   Alonso Sepúlveda Castellanos, et al.

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We determine the Weierstrass semigroup H(P_∞,P_1,…,P_m) at several rational points on the maximal curves which cannot be covered by the Hermitian curve introduced by Tafazolian, Teherán-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.