Abstract
For Quasihermitian curves defined over F 2, with genus g ≥ 1, we present sufficient conditions for getting maximal curves on \({F_{{2^{{2_g}}}}}\). This shows a way to obtain good AG Codes from this class of curves.
R..J. McEliece’s contribution to this paper was supported by NSF grant no. CCR9804793, and grants from the Sony Corp., Qualcomm, Caltech’s Lee Center for Advanced Networking.
M.C. Rodríguez-Palánquex was supported by DGICYT (“Dirección General de Investigación del Ministerio de Ciencia y Tecnología”) under grant TIC2000-0735. During this work M.C. Rodríguez-Palánquex was with the Department of Electrical Engineering at California Institute of Technology. This author would like to express her appreciation to the “Programa Complutense del Amo” (Universidad Complutense de Madrid), for providing her a grant for this stay.
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References
García-Villalba, L.J. & Rodriguez-Palânquex M.C. & MontoyaVitini, F. An Algorithm for Computing the Minimum Distance. Electronics Letters, Vol. 35, No. 18, pp. 1534–1535. 1999.
van Lint, J.H. & van der Geer, G. Introduction to Coding Theory and Algebraic Geometry. Birkhäuser Verlag, Basel. 1988.
MacWilliams, F.J. and Sloane, N.J.A. The Theory of Error Correcting Codes Amsterdam, North-Holland. 1977.
Rodriguez-Palânquex, M.C. Aritmética de Curvas Cuasihermíticas. Aplicaciones a Códigos Geométricos de Goppa. Ph. D. Dissertation Universidad Complutense de Madrid, 1996.
Rodriguez-Palânquex, M.C. and García-Villalba, L.J. and LuengoVelasco, I. Computing the Genus of a Class of Curves. Berlin: Springer-Verlag, 2001. pp. 182–191.
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McEliece, R.J., Rodríguez-Palánquex, M.C. (2002). Results to get Maximal Quasihermitian Curves. New possibilities for AG Codes. In: Blaum, M., Farrell, P.G., van Tilborg, H.C.A. (eds) Information, Coding and Mathematics. The Springer International Series in Engineering and Computer Science, vol 687. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3585-7_4
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DOI: https://doi.org/10.1007/978-1-4757-3585-7_4
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