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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 the Griesmer bound for nonlinear codes
Emanuele Bellini, Eleonora Guerrini, Alessio Meneghetti, Massimi · 2015-01-19 · via cs.IT updates on arXiv.org

Most bounds on the size of codes hold for any code, whether linear or nonlinear. Notably, the Griesmer bound, holds only in the linear case. In this paper we characterize a family of systematic nonlinear codes for which the Griesmer bound holds. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by showing explicit counterexamples. On the other hand, we are also able to provide (weaker) versions of the Griesmer bound holding for all systematic codes.

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