On Curves with Many Rational Points over Finite Fields

Arnaldo Garcia ()
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Arnaldo Garcia: IMPA, Estrada Dona Castorina, 110

A chapter in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, 2002, pp 152-163 from Springer

Abstract: Abstract We summarize results on maximal curves over $${\mathbb{F}_{{q^2}}}$$ (i.e., curves attaining the Hasse-Weil upper bound for the number of rational points over finite fields). We discuss the classification problem and the genus spectrum of maximal curves. We present some towers of curves over finite fields attaining the Drinfeld-Vladut bound. Especially interesting is the description of the completely splitting locus (see Formula (20)) of a certain tower of curves, meaning the first description by their coordinates of the supersingular points of the modular curves X 0(2 n ), for each n ∈ ℕ.

Keywords: Rational Point; Finite Field; Maximal Curve; Compositio Math; Ramification Point (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-59435-9_11

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DOI: 10.1007/978-3-642-59435-9_11

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