AG codes from the second generalization of the GK maximal curve

2019/01/25 by Montanucci, Maria, Lavorante, Vicenzo Pallozzi · 2 citations
#11G20 #11R58 #14H05 #14H55 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.08897

Abstract

The second generalized GK maximal curves GK_2,n are maximal curves over finite fields with q²ⁿ 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 \mathbbF_q²-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 curves 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.

Cited by

• Non-isomorphic subfields of the BM and GGS maximal function fields
• On gap sets in arbitrary Kummer extensions of K(x)

Related

• Two-point AG codes on the GK maximal curves
• AG codes and AG quantum codes from the GGS curve
• AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves
• On AG codes from a generalization of the Deligne-Lustzig curve of Suzuki type
• Weierstrass semigroups at every point of the Suzuki curve