The curve Yn = Xℓ(Xm + 1) over finite fields II

Abstract

Abstract Let F be the finite field of order q2. In this paper we continue the study in [24], [23], [22] of F-maximal curves defined by equations of type yn=xℓ(xm+1). ${{y}^{n}}={{x}^{\ell }}\left( {{x}^{m}}+1 \right).$New results are obtained via certain subcovers of the nonsingular model of vN=ut2−u ${{v}^{N}}={{u}^{{{t}^{2}}}}-u$where q = tα, α ≥ 3 is odd and N = (tα + 1)/(t + 1). We observe that the case α = 3 is closely related to the Giulietti–Korchmáros curve.