On maximal curves

[摘要] We study arithmetical and geometrical properties of maximal curves, that is, curves defined over the finite field F(q)2 whose number of F(q)2-rational points reaches the Hasse-Weil upper bound. Under a hypothesis on non-gaps at a rational point, we prove that maximal curves are F(q)2-isomorphic to y(q) + y = x(m), for some m is an element of Z(+). As a consequence we show that a maximal curve of genus g = (q-1)(2)/4 is F(q)2-isomorphic to the curve y(q) + y = x((q+1)/2). (C) 1997 Academic Press.

[发布日期] 1997-11-01