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Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? 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Two Constructions for Minimal Ternary Linear Codes
Haibo Liu Qunying Liao, Canze Zhu · 2021-07-11 · via cs.IT updates on arXiv.org

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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