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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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On two-weight codes
P. G. Boyvalenkov, K. V. Delchev, D. V. Zinoviev, V. A. Zinoviev · 2020-05-28 · via cs.IT updates on arXiv.org

We consider $q$-ary (linear and nonlinear) block codes with exactly two distances: $d$ and $d+δ$. Several combinatorial constructions of optimal such codes are given. In the linear (but not necessary projective) case, we prove that under certain conditions the existence of such linear $2$-weight code with $δ> 1$ implies the following equality of great common divisors: $(d,q) = (δ,q)$. Upper bounds for the maximum cardinality of such codes are derived by linear programming and from few-distance spherical codes. Tables of lower and upper bounds for small $q = 2,3,4$ and $q\,n < 50$ are presented.

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