### Abstract

Let q be a prime-power, and n≥3 an odd integer. We determine the structure of the Weierstrass semigroup H(P) where P is an arbitrary F_{q2 }-rational point of GK_{2,n} where GK_{2,n} stands for the F_{q2n }-maximal curve of Beelen and Montanucci. We prove that these points are Weierstrass points, and we compute the Frobenius dimension of GK_{2,n}. Using these results, we also show that GK_{2,n} is isomorphic to the Güneri–Garcìa–Stichtenoth only for n=3. Furthermore, AG codes and AG quantum codes from the GK_{2,n} are constructed and discussed. In some cases, they have better parameters compared with those of the known linear codes.

Original language | English |
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Article number | 111810 |

Journal | Discrete Mathematics |

ISSN | 0012-365X |

DOIs | |

Publication status | Accepted/In press - 1 Jan 2020 |

### Keywords

- Algebraic–geometric codes
- Maximal curves
- Weierstrass semigroups

### Cite this

*Discrete Mathematics*, [111810]. https://doi.org/10.1016/j.disc.2020.111810