Asymptotics of Reduced Algebraic Curves Over Finite Fields

J. I. Farrán ()
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J. I. Farrán: Universidad de Valladolid

A chapter in Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 2018, pp 511-523 from Springer

Abstract: Abstract The number A(q) shows the asymptotic behaviour of the quotient of the number of rational points over the genus of non-singular absolutely irreducible curves over 𝔽 q $$\mathbb {F}_{q}\,$$ . Research on bounds for A(q) is closely connected with the so-called asymptotic main problem in Coding Theory. In this paper, we study some generalizations of this number for non-irreducible curves, their connection with A(q) and their application in Coding Theory. We also discuss the possibility of constructing codes from non-irreducible curves, both from theoretical and practical point of view.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-96827-8_22

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DOI: 10.1007/978-3-319-96827-8_22

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