On maximal curves in characteristic two

Details On maximal curves in characteristic two On maximal curves in characteristic two

1998-11-13

arxiv.org/abs/math/9811091v1

Manuscripta Math. 99 (1999), 39--53

Mathematics

Algebraic Geometry

14 pages, LaTex2e

Scientific paper

The genus g of an F_{q^2}-maximal curve satisfies g=g_1:=q(q-1)/2 or g\le g_2:= [(q-1)^2/4]. Previously, such curves with g=g_1 or g=g_2, q odd, have been characterized up to isomorphism. Here it is shown that an F_{q^2}-maximal curve with genus g_2, q even, is F_{q^2}-isomorphic to the nonsingular model of the plane curve \sum_{i=1}^{t}y^{q/2^i}=x^{q+1}, q=2^t, provided that q/2 is a Weierstrass non-gap at some point of the curve.

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