AG codes from $${{\mathbb{F}}_{q^7}}$$-rational points of the GK maximal curve

Abstract In Beelen and Montanucci (Finite Fields Appl 52:10–29, 2018) Giulietti Korchmáros (Math Ann 343:229–245, 2009), Weierstrass semigroups at points of the Giulietti–Korchmáros curve $${\mathcal {X}}$$ X were investigated sets minimal generators determined for all in {X}}(\mathbb {F}_{q^2})$$ ( F q 2 ) {F}_{q^6})\setminus {\mathcal {X}}( \mathbb 6 \ . This paper completes their work by settling remaining cases, that is, {X}}(\overline{\mathbb {F}}_{q}){\setminus }{\mathcal {F}_{q^6})$$ ¯ As an application to AG codes, we determine dimensions lengths duals one-point codes from a point {F}_{q^7}){\setminus {F}_{q})$$ 7 give bound on Feng–Rao minimum distance $$d_{ORD}$$ d ORD For $$q=3$$ = 3 provide table also reports exact values further construct quantum $$\mathbb {F}_{q^7}$$ -rational GK-curve.