On subfields of the second generalization of the GK maximal function field

Abstract

The second generalized GK function fields Kn are a recently found family of maximal function fields over the finite field with q2n elements, where q is a prime power and n≥1 an odd integer. In this paper we construct many new maximal function fields by determining various Galois subfields of Kn. In case gcd⁡(q+1,n)=1 and either q is even or q≡1(mod4), we find a complete list of Galois subfields of Kn. Our construction adds several previously unknown genera to the genus spectrum of maximal curves.