Scholarlink

<p>Linear codes, especially those with few-weight, have extensive applications in cryptography, quantum theory, distributed storage, and combinatorial designs. This paper introduces a new construction of linear codes based on an extended defining set with two trace conditions. The complete weight enumerators and parameters of the codes are determined explicitly, yielding many new two-weight, three-weight, four-weight, and five-weight linear codes with previously unknown parameters. Most of these codes are proven to be minimal via the Ashikhmin–Barg bound and exhibit good performance in cryptographic applications such as secret-sharing schemes.</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

Complete weight enumerators of some few-weight linear codes from extended defining sets

  • 期刊论文

  • 发表日期：

    2026年4月29日

查看全文
  • Shanding Xu,
  • Tianyi Liu,
  • Tong Cui,
  • Gejun Zhu

摘要

Linear codes, especially those with few-weight, have extensive applications in cryptography, quantum theory, distributed storage, and combinatorial designs. This paper introduces a new construction of linear codes based on an extended defining set with two trace conditions. The complete weight enumerators and parameters of the codes are determined explicitly, yielding many new two-weight, three-weight, four-weight, and five-weight linear codes with previously unknown parameters. Most of these codes are proven to be minimal via the Ashikhmin–Barg bound and exhibit good performance in cryptographic applications such as secret-sharing schemes.