2021/07/11 by Liao, Haibo Liu Qunying, Zhu, Canze
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2107.04992
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 \mathbbF3m, 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 \citeHeng-Ding-Zhou.