Some maximal function fields and additive polynomials

GARCİA A., ÖZBUDAK F.

COMMUNICATIONS IN ALGEBRA, vol.35, no.5, pp.1553-1566, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 5
  • Publication Date: 2007
  • Doi Number: 10.1080/00927870601169218
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1553-1566
  • Keywords: additive polynomial, finite field, maximal curve, HERMITIAN CURVE, GENUS
  • Middle East Technical University Affiliated: Yes

Abstract

We derive explicit equations for the maximal function fields F over F-q(2n) given by F = F-q(2n) (X, Y) with the relation A(Y) = f(X), where A(Y) and f(X) are polynomials with coefficients in the finite field F-q(2n), and where A(Y) is q- additive and deg(f) = q(n) + 1. We prove in particular that such maximal function fields F are Galois subfields of the Hermitian function field H over F-q(2n) (i.e., the extension H/F is Galois).