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

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