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Bounding the number of points on a curve using a generalization of Weierstrass semigroups
Año del Documento
Designs, Codes and Cryptography. Volume 66, Issue 1-3, pages 221-230 (2013)
In this article we use techniques from coding theory to derive upper bounds for the number of rational places of the function field of an algebraic curve defined over a finite field. The used techniques yield upper bounds if the (generalized) Weierstrass semigroup for an n-tuple of places is known, even if the exact defining equation of the curve is not known. As shown in examples, this sometimes enables one to get an upper bound for the number of rational places for families of function fields. Our results extend results in [J. Pure Appl. Algebra, 213(6):1152-1156, 2009] .
Revisión por pares
This work was supported in part by the Danish FNU grant 272-07-0266, the Danish National Research Foundation and the National Science Foundation of China (Grant No.11061130539) for the Danish-Chinese Center for Applications of Algebraic Geometry in Coding Theory and Cryptography and by the Spanish grant MTM2007-64704
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