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<p>Galois hulls of linear codes are generalizations of the Euclidean and Hermitian hulls of linear codes. Propagation rules are efficient ways to derive new linear codes from known initial linear codes. In this paper, we combine these two topics and obtain some general results on the dimensions of Galois hulls of linear codes derived from an improved propagation rule. As applications, we further derive many optimal or almost optimal (almost) Galois self-orthogonal codes by employing Galois self-orthogonal maximum distance separable codes and punctured simplex type codes as initial linear codes. In particular, two families of almost Euclidean self-orthogonal binary (near) Griesmer codes are obtained.</p>

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The dimensions of Galois hulls of linear codes derived from an improved propagation rule and related applications

  • 期刊论文

  • 发表日期：

    2025年1月18日

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  • Dengcheng Xie,
  • Yang Li,
  • Shixin Zhu,
  • Yuanting Zhang

摘要

Galois hulls of linear codes are generalizations of the Euclidean and Hermitian hulls of linear codes. Propagation rules are efficient ways to derive new linear codes from known initial linear codes. In this paper, we combine these two topics and obtain some general results on the dimensions of Galois hulls of linear codes derived from an improved propagation rule. As applications, we further derive many optimal or almost optimal (almost) Galois self-orthogonal codes by employing Galois self-orthogonal maximum distance separable codes and punctured simplex type codes as initial linear codes. In particular, two families of almost Euclidean self-orthogonal binary (near) Griesmer codes are obtained.