Construction of Minimal Ternary Linear Codes with Dimension $m+2$ Via Krawtchouk Polynomials
Abstract
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure 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, a generic construction for ternary linear codes with dimension is presented, where is an integer, and a necessary and sufficient condition for this ternary linear code to be minimal is derived. Based on this condition and Krawtchouk Polynomials, a new class of minimal ternary linear codes violating the Ashikhmin-Barg condition are obtained, and then their complete weight enumerators are determined.
Cite
@article{arxiv.2605.14848,
title = {Construction of Minimal Ternary Linear Codes with Dimension $m+2$ Via Krawtchouk Polynomials},
author = {Haibo Liu and Xin Guo and Qunying Liao},
journal= {arXiv preprint arXiv:2605.14848},
year = {2026}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2201.02981