On plane maximal curves
Abstract
The genus of a maximal curve over a finite field with r2 elements is either g0=r(r-1)/2 or less than or equal to g1=(r-1)2/4. Maximal curves with genus g0 or g1 have been characterized up to isomorphism. A natural genus to be studied is g2=(r-1)(r-3)/8, and for this genus there are two non-isomorphism maximal curves known when r 3 (mod 4). Here, a maximal curve with genus g2 and a non-singular plane model is characterized as a Fermat curve of degree (r+1)/2.
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