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<p>In this paper, we introduce a generalized sufficient condition for the self-orthogonality of AG codes, formulated in terms of residues and based on the algebraic structures of finite fields and the geometric properties of algebraic curves. We also present a generic construction of self-orthogonal AG codes from self-dual MDS codes. Using these approaches, we construct several families of self-dual and almost self-dual AG codes. These codes combine two merits: good performance as AG codes whose parameters are close to the Singleton bound, together with Euclidean (or Hermitian) self-dual/self-orthogonal property. Furthermore, some AG codes with Hermitian self-orthogonality can be applied to construct quantum codes with notably good parameters.</p>

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A generic construction on self-orthogonal algebraic geometric codes and its applications

  • 期刊论文

  • 发表日期：

    2026年4月9日

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  • Puyin Wang,
  • Jinquan Luo

摘要

In this paper, we introduce a generalized sufficient condition for the self-orthogonality of AG codes, formulated in terms of residues and based on the algebraic structures of finite fields and the geometric properties of algebraic curves. We also present a generic construction of self-orthogonal AG codes from self-dual MDS codes. Using these approaches, we construct several families of self-dual and almost self-dual AG codes. These codes combine two merits: good performance as AG codes whose parameters are close to the Singleton bound, together with Euclidean (or Hermitian) self-dual/self-orthogonal property. Furthermore, some AG codes with Hermitian self-orthogonality can be applied to construct quantum codes with notably good parameters.