Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, 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, basing on exponential sums, Krawtchouk polynomials, and a function defined on special sets of vectors in $\mathbb{F}_3^m$, we present two new classes of minimal ternary linear codes violating the Ashikhmin-Barg condition, and then determine their complete weight enumerators. Especially, the minimal distance of a class of these codes is better than that of codes constructed in \cite{Heng-Ding-Zhou}.
翻译：最近,由于在秘密共享计划、两方计算等应用中应用了最低线性代码,因此对最低线性代码进行了广泛研究。 建立违反Ashikhmin-Barg条件的最低限度线性代码,然后确定其重量分布,在编码理论和加密中很有意思。 在本文中,基于指数数量,Krawtchouk 多元分子,以及以$\mathbb{F ⁇ 3 ⁇ 3 ⁇ m美美美元中特殊矢量界定的功能,我们提出了两种违反Ashikhmin-Barg条件的新型最低线性代码,然后确定了其完全重量统计器。 特别是,这些代码的最小距离比在\cite{Heng-Ding-Zhou}中构建的代码的距离要好。
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