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<p>Minimal linear codes are of interest due to their wide application in secret sharing schemes and secure two-party computation. In this paper, we construct several families of binary minimal linear codes from generic construction. In this paper, their weight distributions are determined, and the sufficient conditions for them to be minimal are given. It is worth noting that some minimal binary linear codes obtained in this paper violate the Ashikhmin–Barg condition and can be used to design a secret sharing scheme with a good access structure.</p>

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Construction of optimal binary minimal linear codes

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Jiayuan Zhang,
  • Yongsheng Tang,
  • Ping Li,
  • Xiaoshan Kai

摘要

Minimal linear codes are of interest due to their wide application in secret sharing schemes and secure two-party computation. In this paper, we construct several families of binary minimal linear codes from generic construction. In this paper, their weight distributions are determined, and the sufficient conditions for them to be minimal are given. It is worth noting that some minimal binary linear codes obtained in this paper violate the Ashikhmin–Barg condition and can be used to design a secret sharing scheme with a good access structure.