Computing Weierstrass Semigroups and the Feng-Rao Distance from Singular Plane Models

Finite Fields and their Applications

Volumn 6, Issue 1, 2000, Pages 71-92

  Farran J I ^a  

^a UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

Algebraic curves; singular plane models; approximate roots; Abhyankar Moh theorem; Weierstrass semigroups; one point algebraic geometry codes; Ap ry systems; Feng Rao distance.

Indexed keywords

EID: 0010740235     PISSN: 10715797     EISSN: None     Source Type: Journal    
DOI: 10.1006/ffta.1999.0266     Document Type: Article

References (21)

1. Abhyankar S. S. Lectures on Expansion Techniques in Algebraic Geometry. 1977;Tata Institute of Fundamental Research, Bombay.
2. Abhyankar S. S. On the semigroup of a meromorphic curve. Intl. Symp. on Algebraic Geometry. 1977;. p. 249-414.
3. Abhyankar S. S. Irreducibility criterion for germs of analytic functions of two complex variables. Adv. Math. 74:1989;190-257.
4. S. S. Abhyankar and T. T. Moh, Newton-Puiseux expansion and generalised Tschirnhausen transformation, J. Reine Angew. Math.2601973, 47-83, 2611973, 29-54.
5. Angermüller G. Die Wertehalbgruppe einer ebenen irreduziblen algegroiden Kurve. Math. Z. 153:1977;267-282.
6. Apéry R. Sur les branches superlinéaires des courbes algébriques. C.R. Acad. Sci. Paris. 222:1946;1198-1200.
7. Campillo A. Algebroid curves in positive characteristic. Lecture Notes in Math. 813:1980;Springer-Verlag, New York/Berlin.
8. A. Campillo, and, P. Giménez, Syzygies of affine toric varieties, J. Algebra, in press.
9. Farrán J. I. Construcción y decodificación de códigos álgebro-geométricos a partir de curvas planas: algoritmos y aplicaciones. 1997;Univ. Valladolid.
10. Feng G. L., Rao T. R. N. Decoding algebraic-geometric codes up to the designed minimum distance. IEEE Trans. Inform. Theory. 39:1993;37-45.
11. Hansen J. P., Stichtenoth H. Group codes on certain algebraic curves with many rational points. Appl. Algebra Engng. Comm. Comput. 1:1990;67-77.
12. Herzog und J., Kunz E. Die Wertehalbgruppe eines lokalen Rings der Dimension 1. Sitz. Ber. Heidelberger Akad. Wissensch. 2:1971.
13. M. van Hoeij, An Algorithm for Computing an Integral Basis in an Algebraic Function Field, preprint, Maple V Release 4 share library, 1996.
14. Høholdt T., Pellikaan R. On the decoding of algebraic-geometric codes. IEEE Trans. Inform. Theory. 41:1995;1589-1614.
15. T. Høholdt, J. H. van Lint, and R. Pellikaan, Algebraic geometry codes, inHandbook of Coding TheoryV. Pless, W. C. Huffman, and R. A. Brualdi, Eds., Vol. 1 pp. 871-961Elsevier, Amsterdam/New York.
16. Kirfel C., Pellikaan R. The minimum distance of codes in an array coming from telescopic semigroups. IEEE Trans. Inform. Theory. 41:1995;1720-1732.
17. H. Pinkham, Séminaire sur les Singularités des Surfaces (Demazure-Pinkham-Teissier), Cours Donné au Centre de Math. de l'École Polytechnique, 1977-1978.
18. Reguera A. J. Semigroups and clusters at infinity. Progress in Mathematics. 134:1996;Birkhäuser, Basel. p. 339-374.
19. Sathaye A. On planar curves. Amer. J. Math. 99:1977;1105-1135.
20. Trager B. M. Integration of algebraic functions. 1984;Massachusetts Institute of TechnologyDepartment of EECS.
21. Tsfasman M. A., Vlǎdut S. G. Algebraic-geometric codes. Math. and Its Appl. 58:1991;Kluwer Academic, Amsterdam.