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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References:

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