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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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Assumption-Free Theory for Linear Measurements Feedback Lunch: Learned Feedback Codes for Secure Communications On the optimization dynamics of RLVR: Gradient gap and step size thresholds Synthetic Counterfactual Labels for Efficient Conformal Counterfactual Inference Natural Image Classification via Quasi-Cyclic Graph Ensembles and Random-Bond Ising Models at the Nishimori Temperature Multimodal Remote Inference Let's Measure Information Step-by-Step: AI-Based Evaluation Beyond Vibes Best Agent Identification for General Game Playing Optimal Single-Policy Sample Complexity and Transient Coverage for Average-Reward Offline RL MLorc: Momentum Low-rank Compression for Memory Efficient Large Language Model Adaptation Biased Federated Learning under Wireless Heterogeneity MultiTok: Variable-Length Tokenization for Efficient LLMs Adapted from LZW Compression Anomaly Detection from a Tensor Train Perspective Semantic Variational Bayes Based on Semantic Information G Theory for Solving Latent Variables
A Proof of a Conjecture About a Class of Near Maximum Distance Separable Codes
Wei Lu, Xia Wu · 2023-04-09 · via cs.IT updates on arXiv.org

In this paper, we completely determine the number of solutions to $ \operatorname{Tr}^{q^2}_q(bx+b)+c=0, x\in μ_{q+1}\backslash \{-1\}$ for all $b\in \mathbb{F}_{q^2}, c\in\mathbb{F}_{q}$. As an application, we can give the weight distributions of a class of linear codes, and give a completely answer to a recent conjecture about a class of NMDS codes proposed by Heng.

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