Weierstrass Pairs and Minimum Distance of Goppa Codes

@article{Matthews2001WeierstrassPA,
  title={Weierstrass Pairs and Minimum Distance of Goppa Codes},
  author={Gretchen L. Matthews},
  journal={Des. Codes Cryptography},
  year={2001},
  volume={22},
  pages={107-121}
}
We prove that elements of the Weierstrass gap set of a pair of points may be used to define a geometric Goppa code which has minimum distance greater than the usual lower bound. We determine the Weierstrass gap set of a pair of any two Weierstrass points on a Hermitian curve and use this to increase the lower bound on the minimum distance of particular codes defined using a linear combination of the two points. 

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-8 of 8 references

The Weierstrass semigroup of a pair of points on a curve

M. Homma
Arch. Math. 67 • 1996
View 4 Excerpts
Highly Influenced

On the index of the Weierstrass semigroup of a pair of points on a curve

S. J. Kim
Arch. Math. 62 • 1994
View 8 Excerpts
Highly Influenced

On the true minimum distance of Hermitian codes

K. Yang, P. V. Kumar
Coding Theory and Algebraic Geometry, Proceedings, Luminy, 1991, Lecture Notes in Mathematics 1518, Springer-Verlag • 1992
View 7 Excerpts
Highly Influenced

Über die Automorphismengruppe eines algebraischen Funktionenkörpers von Primzahlcharakteristik II

H. Stichtenoth
Arch. Math. 24 • 1973
View 11 Excerpts
Highly Influenced

Geometry and Codes

V. D. Goppa
Kluwer • 1988
View 3 Excerpts

Lax , Consecutive Weierstrass gaps and minimum distance of Goppa codes

S. J. Kim, F. R.
J . Pure Appl . Algebra • 1985

Algebraico-geometric codes

V. D. Goppa
Math. USSR-Izv. 21 • 1983
View 2 Excerpts

Similar Papers

Loading similar papers…