AG codes from the second generalization of the GK maximal curve [article]

Maria Montanucci, Vicenzo Pallozzi Lavorante
2019 arXiv   pre-print
The second generalized GK maximal curves GK_2,n are maximal curves over finite fields with q^2n elements, where q is a prime power and n ≥ 3 an odd integer, constructed by Beelen and Montanucci. In this paper we determine the structure of the Weierstrass semigroup H(P) where P is an arbitrary F_q^2-rational point of GK_2,n. We show that these points are Weierstrass points and the Frobenius dimension of GK_2,n is computed. A new proof of the fact that the first and the second generalized GK
more » ... s are not isomorphic for any n ≥ 5 is obtained. AG codes and AG quantum codes from the curve GK_2,n are constructed; in some cases, they have better parameters with respect to those already known.
arXiv:1901.08897v1 fatcat:r5hphb4r5jgzlfn3xbbaczywcy