Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models
<|reference_start|>Computing Weierstrass semigroups and the Feng-Rao distance from singular plane models: We present an algorithm to compute the Weierstrass semigroup at a point P together with functions for each value in the semigroup, provided P is the only branch at infinity of a singular plane model for the curve. As a byproduct, the method also provides us with a basis for the spaces L(mP) and the computation of the Feng-Rao distance for the corresponding array of geometric Goppa codes. A general computation of the Feng-Rao distance is also obtained. Everything can be applied to the decoding problem by using the majority scheme of Feng and Rao.<|reference_end|>
@article{campillo1999computing,
    title={Computing Weierstrass semigroups and the Feng-Rao distance from singular
  plane models},
    author={A. Campillo and J. I. Farran},
    journal={arXiv preprint arXiv:math/9910155},
    year={1999},
    number={AGT-58},
    archivePrefix={arXiv},
    eprint={math/9910155},
    primaryClass={math.AG cs.IT math.IT math.NA}
}