The second generalized GK maximal curves GK 2,n [1] are maximal curves over finite fields with q 2n elements, where q is a prime power and n ≥ 3 an odd integer. 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 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.

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