Year: 2021
Type: preprint
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}.
Source: arXiv (Cornell University)
Authors: Liao, Haibo Liu Qunying, Zhu, Canze
Institution: Sichuan Normal University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: 剩余码的设计及其相关的编码、译码问题研究
OpenAlex ID: W4287080545