Two Constructions for Minimal Ternary Linear Codes
Information Theory
2021-11-23 v2 math.IT
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 , 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}.
Cite
@article{arxiv.2107.04992,
title = {Two Constructions for Minimal Ternary Linear Codes},
author = {Haibo Liu Qunying Liao and Canze Zhu},
journal= {arXiv preprint arXiv:2107.04992},
year = {2021}
}