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The second generalized Hamming weight for two-point codes on a Hermitian curve

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Abstract

The aim of this article is the determination of the second generalized Hamming weight of any two-point code on a Hermitian curve of degree q + 1. The determination involves results of Coppens on base-point-free pencils on a plane curve. To avoid non- essential trouble, we assume that q > 4.

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Authors and Affiliations

  1. Department of Mathematics, Kanagawa University, Yokohama, 221-8686, Japan

    Masaaki Homma

  2. Department of Mathematics and RINS, Gyeongsang National University, Jinju, 660-701, Korea

    Seon Jeong Kim

Authors
  1. Masaaki Homma
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  2. Seon Jeong Kim
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Correspondence to Masaaki Homma.

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Communicated by J. D. Key.

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Homma, M., Kim, S.J. The second generalized Hamming weight for two-point codes on a Hermitian curve. Des. Codes Cryptogr. 50, 1–40 (2009). https://doi.org/10.1007/s10623-008-9210-x

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  • DOI: https://doi.org/10.1007/s10623-008-9210-x

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