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Yet more projective curves over \(\mathbb F_2\). (English) Zbl 1101.14305

Summary: All plane curves of degree less than 7 with coefficients in \(\mathbb{F}_2\) are examined for curves with a large number of \(\mathbb{F}_g\) rational points on their smooth model, for \(q=2^m, m = 3,4,...,11\). Known lower bounds are improved, and new curves are found meeting or close to Serre’s, Lauter’s, and Ihara’s upper bounds for the maximal number of \(\mathbb{F}_q\) rational points on a curve of genus \(g\).

MSC:

14G15 Finite ground fields in algebraic geometry
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
14G50 Applications to coding theory and cryptography of arithmetic geometry
94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory
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