Abstract
In this paper we introduce the class of semiprimitive Fermat curves, for which Weil-Serre’s bound can be improved using Moreno-Moreno p-adic techniques. The basis of the improvement is a technique for giving the exact divisibility for Fermat curves, by reducing the problem to a simple finite computation.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Moreno, O., Moreno, C.J.: A p-adic Serre Bound. Finite Fields and Their Applications 4, 241–244 (1998)
Moreno, O., Moreno, C.J.: The MacWilliams-Sloane Conjecture on the Tightness of the Carlitz-Uchiyama Bound and the Weights of Duals of BCH Codes. IEEE Trans. Inform. Theory 4(6), 1894–1907 (1994)
Moreno, O., Shum, K., Castro, F.N., Kumar, P.V.: Tight Bounds for Chevalley-Warning-Ax Type Estimates, with Improved Applications. Proc. of the London Mathematical Society 4, 201–217 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Castro, F.N., Gomez, E., Moreno, O. (2006). A Class of Fermat Curves for which Weil-Serre’s Bound Can Be Improved. In: Fossorier, M.P.C., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2006. Lecture Notes in Computer Science, vol 3857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617983_12
Download citation
DOI: https://doi.org/10.1007/11617983_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31423-3
Online ISBN: 978-3-540-31424-0
eBook Packages: Computer ScienceComputer Science (R0)