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Type: Artigo de periódico
Title: On plane maximal curves
Author: Cossidente, A
Hirschfeld, JWP
Korchmaros, G
Torres, F
Abstract: The number N of rational points on an algebraic curve of genus g over a finite field bb F-q satisfies the Hasse-Weil bound N less than or equal to q + 1 +2g root q. A curve that attains this bound is called maximal. With g(0) =1/2(q - root q) and g(1) = 1/4(root q- 1)(2), it is known that maximalcurves have g = g(0) or g less than or equal to g(1). Maximal curves with g = g(0) or g(1) have been characterized up to isomorphism. A natural genus to be studied is g(2) = 1/8(root q - 1)(root q - 3), and for this genus there are two non-isomorphic maximal curves known when root q = 3 (mod 4). Here, a maximal curve with genus g(2) and a non-singular plane model is characterized as a Fermat curve of degree 1/2(root q + 1).
Subject: finite field
maximal curve
linear series
Country: Holanda
Editor: Kluwer Academic Publ
Citation: Compositio Mathematica. Kluwer Academic Publ, v. 121, n. 2, n. 163, n. 181, 2000.
Rights: fechado
Identifier DOI: 10.1023/A:1001826520682
Date Issue: 2000
Appears in Collections:Unicamp - Artigos e Outros Documentos

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