论文标题
最小二进制线性代码的新结构
A New Constructions of Minimal Binary Linear Codes
论文作者
论文摘要
最近，由于其在秘密共享方案，安全的两党计算等方面的应用，因此对最小线性代码进行了广泛的研究。构建最小的线性代码违反了Ashikhmin-Barg条件，然后确定其体重分布在编码理论和加密术中很有趣。在本文中，提出了具有尺寸$ m+2 $的二进制线性代码的通用结构，然后得出该二进制线性代码的必要条件是最小的。基于这种情况和指数总和，获得了一类新的最小二进制线性代码，违反了Ashikhmin-Barg条件，然后确定其权重枚举。
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then determining their weight distributions have been interesting in coding theory and cryptography. In this paper, a generic construction for binary linear codes with dimension $m+2$ is presented, then a necessary and sufficient condition for this binary linear code to be minimal is derived. Based on this condition and exponential sums, a new class of minimal binary linear codes violating the Ashikhmin-Barg condition is obtained, and then their weight enumerators are determined.
