基于部分铺展及其对偶访问结构的维数为n+4的极小二元线性码
Minimal Binary Linear Codes of Dimension n+4 from Partial Spreads and Their Dual Access Structures
浏览论文内容
中文总结 AI 辅助
本文提出基于特殊布尔函数的维数为n+4的极小二元线性码通用构造，利用有限域部分铺展几何性质确定其重量分布，推导极小性充要条件，该类码违反Ashikhmin-Barg条件，适用于高级通信系统。
中文摘要 AI 辅助
极小线性码在秘密共享方案、安全多方计算及密码学中具有重要应用。本文提出一类新的极小二元线性码的通用构造方法，其维数为n+4，构造基于特殊类布尔函数。利用有限域中部分铺展（partial spreads）的几何性质，确定所构造码的明确重量分布与重量枚举式；推导该类码为极小码的充要条件，证明其结构上违反著名的Ashikhmin-Barg条件，因此在高级通信系统中极具应用价值。
英文摘要
Minimal linear codes have significant applications in secret sharing schemes, secure multi-party computation, and cryptography. In this paper, we propose a generic construction of a new family of minimal binary linear codes with dimension n+4 from a special class of Boolean functions. By leveraging the geometric properties of partial spreads in finite fields, we determine the explicit weight distribution and weight enumerator of the constructed codes. Furthermore, we derive a necessary and sufficient condition for these codes to be minimal, and establish that the proposed family yields minimal codes that structurally violate the well-known Ashikhmin-Barg condition, making them highly desirable for advanced communication systems.
