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In this paper, we determine the Weierstrass semigroup $H(P_{\infty})$ and thefull automorphism group of a certain family of curves $\mathcal{X}_{n,r}$,which was recently introduced by Borges and Concei\c{c}\~ao.

Weierstrass semigroup and Automorphism group of the curves $\mathcal{X}_{n,r}$