Scholarlink

<p>In this paper, we study 1-generator quasi-twisted (QT) codes with their <i>k</i>-Galois duals. We obtain the generating set of <i>k</i>-Galois dual codes of 1-generator QT codes under some restrictions. Further, we get necessary and sufficient conditions for 1-generator QT codes to be Galois self-orthogonal and Galois self-dual. We prove that Galois self-orthogonal QT codes are asymptotically good. Some optimal and near optimal self-dual 1-generator QT codes are obtained. As an application, we construct some new quantum codes using Galois self-orthogonal 1-generator QT codes.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Galois duals of 1-generator quasi-twisted codes and their applications in quantum codes construction

  • 期刊论文

  • 发表日期：

    2026年1月9日

查看全文
  • Yongkang Shao,
  • Jian Gao,
  • Jiafu Mi,
  • Weiqi Shao

摘要

In this paper, we study 1-generator quasi-twisted (QT) codes with their k-Galois duals. We obtain the generating set of k-Galois dual codes of 1-generator QT codes under some restrictions. Further, we get necessary and sufficient conditions for 1-generator QT codes to be Galois self-orthogonal and Galois self-dual. We prove that Galois self-orthogonal QT codes are asymptotically good. Some optimal and near optimal self-dual 1-generator QT codes are obtained. As an application, we construct some new quantum codes using Galois self-orthogonal 1-generator QT codes.