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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? Exact Structure of Binary Test-Time Aggregation When Semantic Communication Meets Queueing: Cross-Layer Latency and Task Fidelity Optimization Convexity in Disguise: A Theoretical Framework for Nonconvex Low-Rank Matrix Estimation Conditional Diffusion Under Linear Constraints: Langevin Mixing and Information-Theoretic Guarantees Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Expert Routing for Communication-Efficient MoE via Finite Expert Banks Contextual Memory-Enhanced Source Coding for Low-SNR Communications Realizable Bayes-Consistency for General Metric Losses Leveraging Code Automorphisms for Improved Syndrome-Based Neural Decoding A Hierarchical Sampling Framework for bounding the Generalization Error of Federated Learning Dueling DDQN-Based Adaptive Multi-Objective Handover Optimization for LEO Satellite Networks The Causal Description Gap: Information-Theoretic Separations Across Pearl's Hierarchy Optimization of CV-QKD Under Practical Constraints Benchmarking Wireless Representations: High-Dimensional vs. Compressed Embeddings for Efficiency and Robustness Real-Time Text Transmission via LLM-Based Entropy Coding over Fixed-Rate Channels SwiftChannel: Algorithm-Hardware Co-Design for Deep Learning-Based 5G Channel Estimation Evolving Token Communication with Parametric Memory Network Remote Action Generation: Remote Control with Minimal Communication The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions Stabilizing Private LASSO under Heterogeneous Covariates via Anisotropic Objective Perturbation Linear-Readout Floors and Threshold Recovery in Computation in Superposition Soft Graph Diffusion Transformer for MIMO Detection Hierarchical Federated Learning for Networked AI: From Communication Saving to Architecture-Aware Design Exponential families from a single KL identity MIFair: A Mutual-Information Framework for Intersectionality and Multiclass Fairness Diffusion-OAMP for Joint Image Compression and Wireless Transmission Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing Why Self-Supervised Encoders Want to Be Normal Statistical Channel Fingerprint Construction for Massive MIMO: A Unified Tensor Learning Framework Adaptive Transform Coding for Semantic Compression Lightweight Quantum Agent for Edge Systems: Joint PQC and NOMA Resource Allocation Rethinking KV Cache Eviction via a Unified Information-Theoretic Objective Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data MEG-RAG: Quantifying Multi-modal Evidence Grounding for Evidence Selection in RAG Generalising maximum mean discrepancy: kernelised functional Bregman divergences Improving Robustness of Tabular Retrieval via Representational Stability Information-Theoretic Measures in AI: A Practical Decision Guide A Unified Fractional Regularization Framework for Sparse Recovery Shape of Memory: a Geometric Analysis of Machine Unlearning in Second-Order Optimizers The Exact Replica Threshold for Nonlinear Moments of Quantum States Semantic Error Correction and Decoding for Short Block Codes Null-Space Flow Matching for MIMO Channel Estimation in Latency-Constrained Systems Directional Confusions Reveal Divergent Inductive Biases Through Rate-Distortion Geometry in Human and Machine Vision MambaCSP: Hybrid-Attention State Space Models for Hardware-Efficient Channel State Prediction Amortized Vine Copulas for High-Dimensional Density and Information Estimation Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithms Secure Rate-Distortion-Perception: A Randomized Distributed Function Computation Approach for Realism RateQuant: Optimal Mixed-Precision KV Cache Quantization via Rate-Distortion Theory FB-NLL: A Feature-Based Approach to Tackle Noisy Labels in Personalized Federated Learning Ultrametric OGP - 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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
Linear codes with two or three weights from weakly regular bent functions
Chunming Tang, Nian Li, Yanfeng Qi, Zhengchun Zhou, Tor Helleset · 2015-07-22 · via cs.IT updates on arXiv.org

Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of constructing two-weight and three-weight linear codes of Ding et al. \cite{DD2015} and Zhou et al. \cite{ZLFH2015} to general weakly regular bent functions and determines the weight distributions of these linear codes. It solves the open problem of Ding et al. \cite{DD2015}. Further, this paper constructs new linear codes with two or three weights and presents the weight distributions of these codes. They contains some optimal codes meeting certain bound on linear codes.

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