Two Constructions for Minimal Ternary Linear Codes

Haibo Liu Qunying Liao; Canze Zhu

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arXiv · 2107.04992

Two Constructions for Minimal Ternary Linear Codes

Haibo Liu Qunying Liao·Canze Zhu

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Abstract

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}.

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Haibo Liu Qunying Liao, Canze Zhu. 2021-11-21. Two Constructions for Minimal Ternary Linear Codes. https://arxiv.org/abs/2107.04992

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