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<p>In this paper, we establish a necessary and sufficient condition for a subgroup to constitute a perfect code in the setting of finite groups. As an application, we completely classify all subgroup perfect codes for extraspecial 2-groups, as well as for finite groups whose Sylow 2-subgroups are extraspecial.</p>

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Classification of Subgroup Perfect Codes in Cayley Graphs

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Jingjian Li,
  • Binbin Li,
  • Xianglin Liu

摘要

In this paper, we establish a necessary and sufficient condition for a subgroup to constitute a perfect code in the setting of finite groups. As an application, we completely classify all subgroup perfect codes for extraspecial 2-groups, as well as for finite groups whose Sylow 2-subgroups are extraspecial.