Abstract
We present a method for effective construction of algebraic-geometric codes based on the Brill-Noether algorithm. This paper is based on a paper by Le Brigand and Risler [8], but the presentation uses only the theory of algebraic function fields of one variable.
Preview
Unable to display preview. Download preview PDF.
References
M. Bronstein, M. Hassner, A. Vasquez and C.J. Williamson, Algebraic algorithms for the construction of error correction codes on algebraic curves, Proceedings of IEEE International Symposium on Information Theory, June 1991.
W. Fulton, Algebraic curves: An introduction to algebraic geometry, W.A. Benjamin, Inc, New-York, Amsterdam, 1969.
V.D. Goppa, Codes associated with divisors, Probl. Peredach. infor., 13(1):33–39, 1977.
D. Gorenstein, An arithmetic theory of adjoint plane curves, Trans. Amer. Math. Soc. 72 (1952), 414–436.
G. Haché and D. Le Brigand, Effective Construction of Algebraic Geometry Codes, Technical Report 2267, INRIA, May 1994.
H. Hironaka, On the arithmetic genera and the effective genera of algebraic curves, Memoirs of the College of Sciences of Kyoto, Series A, 30, Math. 2 (1957),177–195.
D. Lazard, Solving zero-dimensional algebraic systems, J. Symbolic Cumputation, 13, 1992.
D. Le Brigand and J.J. Risler, Algorithme de Brill-Noether et codes de Goppa, Bull. Soc. math. France, 116 (1988), 231–253.
D. Polemi, M. Hassner, O. Moreno and C.J. Williamson, A computer algebra algorithm for the adjoint divisor, Proceedings of IEEE International Symposium on Information Theory, January 1993.
H. Stichtenoth, Algebraic function fields and codes, University Text, Springer-Verlag, 1993.
M.Tsfasman and S. Vladut, Algebraic-geometric codes, Kluwer Academic Pub., Math. and its Appl. 58, 1991.
A.T. Vasquez, Rational desingularization of a curve defined over a finite field, Number Theory, N. Y. Seminar 1989–1990, Springer-Verlag, 229–250.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Haché, G. (1995). Computation in algebraic function fields for effective construction of algebraic-geometric codes. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_19
Download citation
DOI: https://doi.org/10.1007/3-540-60114-7_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60114-2
Online ISBN: 978-3-540-49440-9
eBook Packages: Springer Book Archive