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

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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 (mod 4), we find a complete list of Galois subfields of Kn. Our construction adds several previously unknown genera to the genus spectrum of maximal curves
Original languageEnglish
Article number101669
JournalFinite fields and their applications
Volume64
Number of pages24
ISSN1071-5797
DOIs
Publication statusPublished - 2020

Keywords

  • Second generalized
  • Giulietti–Korchmáros function fields
  • Genus spectrum of maximal curves

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