Two Classes of Minimal Ternary Linear Codes and Their Complete Enumerators
Two Classes of Minimal Ternary Linear Codes and Their Complete Enumerators
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两类最小三进制线性码及其完整枚举器
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通讯作者：
朱灿泽
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作者：
刘海波;廖群英;朱灿泽
近年来，极小线性码由于在秘密共享方案、两方计算等方面的应用而得到了广泛的研究。构造不满足Ashikhmin-Barg条件的极小线性码并确定其重量分布是编码理论和密码学中的一个重要问题。本文利用指数和、Krawtchouk多项式以及定义在$\mathbb{F} 3 ^m $中特殊向量集上的函数，提出了两类新的不满足Ashikhmin-Barg条件的极小三元线性码，并确定了它们的完备权计数元.
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, two-party computations. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then determining their weight distributions are 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.