ASDSApplied Statistics and Data Science3066-84333066-8441Art and Technology10.61369/ASDS.2026010008Article线性秘密共享中的自对偶结构https://artdesignp.com/journal/ASDS/2/1/10.61369/ASDS.2026010008林群2026212026-01-20线性秘密共享方案（LSSS）是现代密码学中支撑安全多方计算与密码协议的关键基础。本文旨在系统性地构建一个基于线性码的LSSS 理论框架。首先，形式化线性秘密共享方案，阐述了份额生成与秘密重构的算法流程。其次，阐明了线性码的理论基础，明确了生成矩阵与校验矩阵的核心作用。本文的贡献在于探讨了自对偶码的数学性质，并通过一个具体的二元域实例加以验证。自对偶码因其内在的对称性和优美的结构，为构建高效安全的线性秘密共享方案提供了理论工具，在信息安全及相关领域中具有重要的应用价值。线性秘密共享,访问结构,生成矩阵,自对偶码

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