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Designs, Codes and Cryptography

, Volume 76, Issue 1, pp 81–87 | Cite as

The second generalized Hamming weight of certain Castle codes

  • Wilson Olaya-LeónEmail author
  • Claudia Granados-Pinzón
Article

Abstract

We compute the bound \(d_2 ^*\) on the second generalized Hamming weight for some AG codes coming from Castle curves. We consider those codes related to Weierstrass semigroups generated by two integers. Important codes as Hermitian, Norm-Trace and certain hyperelliptic codes belong to this class of codes. We obtain a simple characterization for the true values of the second generalized Hamming weight of all Hermitian codes.

Keywords

Error-correcting codes AG codes Castle codes  Generalized Hamming weights Hermitian codes 

Mathematics Subject Classification

94A27 94B65 

Notes

Acknowledgments

The authors wish to thank Professor Carlos Munuera for his useful discussions. We also wish to thank the referees for many interesting comments.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Escuela de MatemáticasUniversidad Industrial de SantanderBucaramangaColombia

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