AG codes from the second generalization of the GK maximal curve

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 Fq2-rational point of GK2,n where GK2,n stands for the Fq2n-maximal curve of Beelen and Montanucci. We prove that these points are Weierstrass points, and we compute the Frobenius dimension of GK2,n. Using these results, we also show that GK2,n is isomorphic to the Güneri–Garcìa–Stichtenoth only for n=3. Furthermore, AG codes and AG quantum codes from the GK2,n are constructed and discussed. In some cases, they have better parameters compared with those of the known linear codes.