Abstract
We determine the Weierstrass semigroup of a pair of rational points on Norm-Trace curves. We use this semigroup to improve the lower bound on the minimum distance of two-point algebraic geometry codes arising from these curves.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Carvalho, C., Torres, F.: On Goppa codes and Weierstrass gaps at several points. Designs, Codes and Cryptography 35, 211–225 (2005)
Garcia, A., Kim, S.J., Lax, R.F.: Consecutive Weierstrass gaps and minimum distance of Goppa codes. J. Pure Applied Algebra 84, 199–207 (1993)
Geil, O.: On codes from norm-trace curves. Finite Fields and Their Applications 9, 351–371 (2003)
Hansen, J.P., Stichtenoth, H.: Group codes on certain curves with many rational points. Applicable Algebra Eng. Comm. Computing 1, 67–77 (1990)
Høholdt, T., van Lint, J., Pellikaan, R.: Algebraic geometry codes. In: Pless, V.S., Huffman, W.C. (eds.) Handbook of Coding Theory, vol. 1. Elsevier, Amsterdam (1998)
Homma, M., Kim, S.J.: Goppa codes with Weierstrass pairs. J. Pure Applied Algebra 162, 273–290 (2001)
Homma, M.: The Weierstrass semigroup of a pair of points on a curve. Archiv. Math. 67, 337–348 (1996)
Kim, S.J.: On index of the Weierstrass semigroup of a pair of points on a curve. Archiv. Math. 62, 73–82 (1994)
Matthews, G.L.: Codes from the Suzuki function field. IEEE Transactions on Information Theory 50, 3298–3302 (2004)
Matthews, G.L.: Weierstrass pairs and minimum distance of Goppa codes. Designs, Codes and Cryptography 22, 107–121 (2001)
Stightenoth, H.: Algebraic function fields and codes. Springer, Berlin (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Munuera, C., Tizziotti, G.C., Torres, F. (2008). Two-Point Codes on Norm-Trace Curves. In: Barbero, Á. (eds) Coding Theory and Applications. Lecture Notes in Computer Science, vol 5228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87448-5_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-87448-5_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87447-8
Online ISBN: 978-3-540-87448-5
eBook Packages: Computer ScienceComputer Science (R0)