Symbolic Hamburger-Noether expressions of plane curves and applications to AG codes

Authors:
A. Campillo;J. I. Farrán
Affiliations:
Departamento de Algebra, Geometría y Topología, Universidad de Valladolid, Spain;Departamento de Matemática Aplicada a la Ingeniería, Universidad de Valladolid, Spain
Venue:
Mathematics of Computation
Year:
2002

Citing 8
Cited 3

Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve (extended abstract)

SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Algebraic-Geometric Codes

Algebraic-Geometric Codes
Computation in Algebraic Function Fields for Effective Construction of Algebraic-Geometric Codes

AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
SINGULAR: a computer algebra system for polynomial computations

ACM Communications in Computer Algebra
On the decoding of algebraic-geometric codes

IEEE Transactions on Information Theory - Part 1
Effective construction of algebraic geometry codes

IEEE Transactions on Information Theory - Part 1
The minimum distance of codes in an array coming from telescopic semigroups

IEEE Transactions on Information Theory - Part 1
Computing Weierstrass Semigroups and the Feng-Rao Distance from Singular Plane Models

Finite Fields and Their Applications

Evaluation codes and plane valuations

Designs, Codes and Cryptography
Formal desingularization of surfaces: The Jung method revisited

Journal of Symbolic Computation
Computational aspects of retrieving a representation of an algebraic geometry code

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we consider some practical applications of the symbolic Hamburger-Noether expressions for plane curves, which are introduced as a symbolic version of the so-called Hamburger-Noether expansions. More precisely, we give and develop in symbolic terms algorithms to compute the resolution tree of a plane curve (and the adjunction divisor, in particular), rational parametrizations for the branches of such a curve, special adjoints with assigned conditions (connected with different problems, like the so-called Brill-Noether algorithm), and the Weierstrass semigroup at P together with functions for each value in this semigroup, provided P is a rational branch of a singular plane model for the curve. Some other computational problems related to algebraic curves over perfect fields can be treated symbolically by means of such expressions, but we deal just with those connected with the effective construction and decoding of algebraic geometry codes.