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arXiv2026

CARDINAL Predicts Cardiovascular Risk From Non-contrast Cardiac CT

Cardiovascular risk prediction remains limited by incomplete clinical data and imaging biomarkers that reduce computed tomography (CT) to a small number of handcrafted features. We developed CARDINAL (Cardiovascular Assessment via Representation learning from Deep Imaging with Nested Anatomical Latent embeddings), a clinically grounded framework that learns compact representations from routine non-contrast cardiac CT for major adverse cardiovascular event (MACE) prediction. In 17,659 patients, CARDINAL was evaluated for 1-, 3-, 5-, and 10-year MACE prediction against American Heart Association (AHA) pooled cohort equations (PCE), AHA predicting risk of cardiovascular disease events (PREVENT), coronary artery calcium (CAC), segmentation-derived CT biomarkers, and 70-feature structural radiomics. Gains were largest at longer horizons. At 10 years, CARDINAL (joint) achieved an area under the receiver operating characteristic curve (AUROC) of 0.866 $\pm$ 0.020 and an area under the precision-recall curve (AUPRC) of 0.890 $\pm$ 0.015, compared with an AUROC of 0.826 $\pm$ 0.023 and an AUPRC of 0.826 $\pm$ 0.022 for structural radiomics, the strongest baseline. CARDINAL also achieved the highest survival concordance index (C-index), 0.753 $\pm$ 0.015, and high-versus-low risk-tertile hazard ratio, 10.78 $\pm$ 3.16, with favorable reclassification and exploratory calibration. These findings suggest that non-contrast cardiac CT contains prognostic information beyond conventional risk equations, CAC scoring, and engineered imaging biomarkers.

eess.IV↗
arXiv2026

Patient-Specific Articulated Digital Twins from a Single Full-Body CT Scan

Patient-specific anatomical models provide individualized context for surgical planning, image-guided intervention, and algorithm development. However, most CT-derived models are static: they preserve the body configuration captured at scan time, but cannot represent how the same anatomy would appear after patient repositioning. This limitation is especially important for radiographic imaging, where appearance depends jointly on imaging geometry and patient pose. We present a proof-of-concept for constructing a patient-specific \emph{articulated} digital twin from a single full-body CT scan. The method fits a parametric human body model (SMPL) to obtain a patient-aligned kinematic scaffold, binds segmented bones and organs to an anatomy-aware rig, and retargets body-pose changes while preserving skeletal geometry. Using full-body CT scans from three subjects, the fitted scaffold achieved 15.8 $\pm$ 4.0 mm chamfer distance and 95.9 $\pm$ 1.8\% skeletal enclosure. Recomposition at the acquisition pose preserved major radiographic structure, with overall SSIM of 0.872 $\pm$ 0.016 and PSNR of 18.5 $\pm$ 1.4 dB across paired DRRs. Across unseen target poses, the resulting twins enabled articulation while maintaining high skeletal enclosure (94.4 $\pm$ 0.4\%). As a feasibility demonstration, we render the articulated twin as pose-dependent DRRs. These results suggest the feasibility of extending static, view-controllable CT simulation toward pose-controllable anatomical twins for future synthetic imaging and positioning studies.

cs.CV↗
arXiv2026

Integrality Gap Bounds for the Goemans-Linial SDP on Finite Abelian Cayley Graphs

In the uniform sparsest cut problem we are asked to find a vertex set that cuts few edges relative to the number of vertex pairs it separates. The Goemans-Linial SDP coupled with the Arora-Rao-Vazirani rounding gives an $\mathcal{O}(\sqrt{\log n})$ approximation on arbitrary graphs on $n$ vertices. We study this relaxation on finite Abelian Cayley graphs. First we show that when the second normalized Laplacian eigenvalue of $G= \mathrm{Cayley}(Γ, S)$ is realized by a Fourier character with image size at most four then $λ_2(G)=\mathrm{SDP}_{\mathrm{GL}}(G)=ψ(G)$. Geometrically, a character maps the vertices onto a regular polygon where the squared chord distance satisfies the triangle inequalities exactly when the polygon has at most four vertices. Grouping equal character fibers gives a cyclic quotient where the optimal cut can be found exactly and so the relaxation is exact on finite Abelian Cayley graphs on groups of exponent at most four. Second, we replace each generator $s$ of $S$ by a uniformly random element of its cyclic subgroup (including identity). If $r_s$ is the order of $s$, we let $α(r_s)$ to be the average number of $\pm s$ steps needed to simulate such a move, and let $ρ(S)=\max_{s\in S}α(r_s)$ be its worst case. Full cyclic averaging eliminates character phases and choosing a nontrivial character $χ^*$ minimizing the auxiliary eigenvalue and taking $K=\mathrm{ker}χ^*$ gives \[ ψ(G)\leqψ_G(K)\leq\frac{q^*}{q^*-1} \cdotρ(S)\cdot\mathrm{SDP}_{\mathrm{GL}}(G)\leq 2ρ(S)\cdot\mathrm{SDP}_{\mathrm{GL}}(G), \] where $q^*=|χ^*(Γ)|$. If all generator orders are at most $R$, this is an $R/2$ approximation. Finally, we construct an infinite family of finite Abelian Cayley graphs with Goemans-Linial integrality gap exactly $16/15$.

math.CO↗
arXiv2026

Lightweight Adaptation of EEG Foundation Models for Stroke Motor Imagery Decoding: Domain Shift and Subject-Level Robustness

Motor imagery (MI) electroencephalography (EEG) decoding could support post-stroke rehabilitation, but models developed on healthy cohorts may not transfer reliably to pathological EEG. We evaluated whether Low-Rank Adaptation (LoRA) can efficiently adapt three pretrained EEG foundation models (i.e., LaBraM-base, REVE-base, and REVE-large) for binary left- versus right-hand MI decoding. Frozen-backbone head-only baselines and LoRA adaptation were evaluated using subject-wise five-fold cross-validation on the PhysioNet EEG Motor Movement/Imagery Dataset and a binary subset of the UET175 dataset comprising 30 stroke participants. On EEGMMIDB, LoRA increased accuracy to 0.822 for LaBraM-base and 0.957 for REVE-base. On UET175, all head-only models performed near chance. With LoRA, LaBraM-base remained near chance (0.499$\pm$0.009), whereas REVE-base reached 0.847$\pm$0.194 and outperformed REVE-large (0.806$\pm$0.178), indicating that increased model capacity alone did not improve stroke-domain adaptation. The strongest stroke configuration, REVE-base LoRA, was further evaluated using within-cohort leave-one-subject-out cross-validation (LOOCV), showing 0.952 mean accuracy, but subject-wise accuracy ranged from 0.586 to 1.000, revealing a small low-performing tail. Zero-shot transfer from EEGMMIDB to UET175 remained near chance (0.464$\pm$0.072). These findings show that healthy-benchmark performance does not ensure transfer to stroke EEG. Translation of EEG foundation models to pseudo-online or real-time rehabilitation BCIs should therefore include target-domain adaptation and subject-level assessment of temporal informativeness, spatial sensitivity, and physiological discriminability.

cs.CE↗
arXiv2026

Automated Event Log Generation from Unstructured Text Using Finetuned LLMs

Process mining (PM) provides a powerful framework for discovering and optimizing operational processes from event data. However, the efficacy of PM techniques is strictly predicated on the availability of structured event logs. Thus far, event logs have often been laboriously created by domain and process mining experts. This costly effort causes large portions of organizational knowledge, including incident tickets, manuals, and textual reports, to remain underutilized. We address this bottleneck by investigating the efficacy of Large Language Models (LLMs) as automated data translators. We propose a scalable framework that leverages LLMs as data translators to bridge the gap between unstructured textual resources and structured event data. We finetune LLMs on a newly created text-to-log dataset, demonstrating that the resulting models can extract high-fidelity event logs from unstructured resources. Our results show that this finetuning approach outperforms few-shot or zero-shot prompting by a large amount, highlighting finetuning as a necessary pre-condition for generating reliable event data. We conclude that our method provides a promising pipeline for making previously unused data available to process mining ecosystems, effectively expanding the possibilities of using PM to further investigate organizational workflows.

cs.AI↗
arXiv2026

REFACTOR-VLA: Unsupervised Library Learning of Typed Motor Programs

Most vision-language-action (VLA) models -- OpenVLA, $π_0$, RT-2, RDT-1B -- are monolithic: they emit raw motor commands or short action chunks without organizing behavior into reusable abstractions, so they degrade on long-horizon tasks and resist interpretation. Existing skill-discovery methods sidestep the core question of when two action sequences are behaviorally equivalent, either clustering contrastive embeddings or delegating the judgment to a language model uncalibrated to the robot's dynamics. We introduce REFACTOR-VLA, a wake/sleep system for learning reusable skills. Its sleep phase clusters motor-program fragments under a Behavioral-Equivalence Kernel (BEK) computed from rollouts of a learned latent world model $M_ϕ$; its wake phase emits typed lambda terms over a Hindley--Milner-inspired vocabulary, consumed by a library-conditioned rectified-flow action decoder. Abstractions are admitted only if they pass Minimum Description Length and return-preservation gates. On LIBERO we report two findings. First, enlarging the world model from 188M to 430M parameters worsened performance on 4 of 4 suites, so capacity alone does not help. Second, the training objective matters far more: adding an auxiliary supervised contrastive (InfoNCE) loss during world-model warmup substantially improves sleep-phase clustering, giving Normalized Mutual Information at $n=3$ seeds of $0.462 \pm 0.021$ (object), $0.867 \pm 0.025$ (spatial), $0.915 \pm 0.013$ (goal) and $0.754 \pm 0.010$ (LIBERO-10), and beating the strongest published baseline on all 4 suites by a mean $Δ= +0.184$. Across providers ($n=12$) the 95% bootstrap confidence interval for mean pairwise NMI is $[0.683, 0.729]$ (mean $0.705$). The sleep phase also yields the first real-LIBERO task-language library: the decoder uses 2 of 3 admitted abstractions and rewrites all 256 sampled demonstrations.

cs.LG↗
arXiv2026

Mesh-Native Physics-Informed Graph Surrogates for TCAD-in-the-Loop Design Space Exploration

High-fidelity TCAD simulation of drift-diffusion transport remains the workhorse of emerging FinFET device design, but it is computationally expensive, especially for 3D structures where runtime escalates steeply with mesh complexity. This sharply limits multi-objective design space exploration. Existing machine-learning surrogates map a fixed set of design parameters to a few scalar device metrics, discarding the underlying physics and losing transferability across device geometries and families. A physics-informed graph attention network (GAT) surrogate is proposed. It operates directly on the tetrahedral TCAD mesh and predicts, at every mesh node, the electrostatic potential together with the electron and hole quasi-Fermi levels, the fundamental unknowns of the drift-diffusion system. Training combines a data loss with finite-volume current-continuity residuals, embedding carrier-transport physics into the objective. Operating on the mesh as a graph, the surrogate inherits size generalization: a model trained on few-fin meshes applies unchanged to substantially larger arrays, bounded at inference only by GPU memory. Per-node uncertainty from a deep ensemble drives an active-learning loop that screens large candidate pools in seconds and forwards only the most informative designs for full simulation. Benchmarked against Sentaurus Device on multi-fin tri-gate FinFETs, the surrogate reproduces the three drift-diffusion fields with sub-volt per-field RMSE and reaches a per-design throughput orders of magnitude higher than the full simulator. The advantage grows with device size: on large multi-fin arrays that are prohibitively slow to simulate directly, inference still completes in under a second per device, enabling Pareto-front exploration across device scales infeasible for direct TCAD sweeps.

cs.LG↗
arXiv2026

Thermal Imaging for Contactless Cardiorespiratory and Sudomotor Response Monitoring

Human-machine interfaces in industrial automation need sensing modules that monitor operator actions and physiological state. This is important in factories, vehicles, machinery cabins, and human-robot collaboration, where workload, stress, fatigue, or reduced attention can affect safety. RGB monitoring is limited by low light, shadows, and privacy concerns, while thermal infrared imaging captures skin temperature dynamics without visible illumination. This paper studies thermal video as a contactless computer vision modality for estimating electrodermal activity (EDA), heart rate (HR), and breathing rate (BR), with the goal of supporting adaptive human-machine interfaces and operator-state awareness. We propose a signal-processing pipeline that tracks facial regions, aggregates thermal signals, and separates slow sudomotor trends from faster cardiorespiratory components. HR is estimated using orthogonal matrix image transformation (OMIT) across multiple facial regions, while BR is estimated from nasal and cheek thermal signals using spectral peak detection. We characterize 288 ROI-method configurations against contact references with lag-tolerant metrics using 31 sessions from the public SIMULATOR STUDY 1 (SIM1) driver monitoring dataset. The best fixed EDA configuration reaches a mean absolute correlation of $0.40 \pm 0.23$ against palm EDA, with individual sessions reaching $0.89$. BR estimation achieves $3.1 \pm 1.1$ bpm mean absolute error, while HR estimation yields $13.8 \pm 7.5$ bpm MAE, limited by the $7.5$ Hz thermal camera frame rate. The results show that thermal video provides useful respiratory and sudomotor cues, while revealing limitations caused by ROI selection, polarity changes, latency, and subject variability. These findings provide baseline design guidance for thermal computer vision as an auxiliary sensing layer in adaptive industrial HMI systems.

cs.CV↗
arXiv2026

Does Your Agent's Memory Survive a Model Upgrade? A Controlled Study of Memory Portability

Model upgrades are routine; memory migrations are not. An agent can keep the same memory store and still forget: a new model may interpret old notes differently, mixed embedding versions may break retrieval, and repair may fail without the original evidence. We compare memory as the same history is preserved verbatim for long-context reading (LC-RAW), divided into chunks for retrieval-augmented generation (RAG), compressed by a model into natural-language notes (NOTES), or normalized into a fixed-schema knowledge graph (KG-fixed). The study uses 48 synthetic histories with randomized answer codes, exact scoring, and two open-weight models with sub 10 billion parameters. Our measurements show that fixed-schema structures transfer reliably, with KG-fixed accuracy changing by only $+0.0004 \pm 0.0020$ following a writer swap. Conversely, compressed NOTES exhibit high model coupling, with accuracy shifting asymmetrically by $+9.91$ or $-13.28$ percentage points depending on the specific migration direction. In RAG systems, partial embedding migrations using a 50/50 mixed index capture only a 4.96-point accuracy improvement, forfeiting the majority of the 11.90-point gain achieved through full re-embedding. Diagnostic decomposition attributes 80% ($0.467 \pm 0.014$) of the NOTES accuracy deficit to information lost during initial construction, whereas retrieval failures drive 81% ($0.364 \pm 0.012$) of the RAG deficit. Finally, store-only repair of NOTES fails to reach a 90% performance recovery target in all 48 test cases, whereas retaining the raw source history enables successful recovery in 34 of 48 cases for one tested direction. These findings highlight the necessity of direction-specific migration testing, strict embedding space isolation, and the retention of source histories for memory repair.

cs.AI↗
arXiv2026

Making Prospective Memory SLM-Shaped: Typed Intention Stores for Small-Model Agents

Prospective memory means carrying out a deferred intention at the right future cue while other work continues. Benchmarks now isolate it as an agent skill, yet frontier LLMs still struggle: the best published PM-Bench scaffold reaches only 65.1% Set-F1. We argue that this loop is schema-constrained state tracking rather than open-ended reasoning, and that small models can execute it when the action space is typed. We propose the Prospective Intention Store (PIS) that puts lifecycle logic in code and scoped language work on the model. The scaffold is agentic and training-free: no selector fine-tuning and no trajectory distillation. On PM-Bench, DeepSeek-Chat with PIS reaches 82.9% Set-F1. On Gemma-E2B, Set-F1 is only 4.2% without a store and at most 6.6% under seven retrospective memories, while PIS reaches 66.2%. PIS further reaches 70.1% Set-F1, where retrospective memory methods stay at most 54.4%. PIS sets a new state of the art on this benchmark and enables small models to surpass the published large-model scaffold.

cs.AI↗
arXiv2026

Patterning in Practice: Debiasing Reward Models with Susceptibilities

Reward models trained on human preferences are known to suffer from length, formatting, and other stylistic biases. In this paper we use patterning, which reweights each preference pair according to its measured effect on posterior expectation values of benchmark losses (its susceptibility), to debias a Gemma 2 9B Instruct reward model trained on Skywork-Reward-Preference v0.2. We obtain $+14.2 \pm 1.2$ pp on RM-Bench Hard, the split where style cues point against correctness (mean $\pm$ s.e.\ over 5 seeds), with overall RM-Bench accuracy preserved, comparable to the strongest Hard-split gain reported by the closest published comparator (SteerRM, $+13.2$ pp). We demonstrate in a simple case that the reweighting is interpretable by tracing a side effect of the intervention (a regression on a safety subset of RM-Bench) to a small class of training pairs, which we confirm by ablation. The weights also transfer: those computed on Gemma 2 9B debias Gemma 2 2B and 27B with no recomputation, and transfer partially to Llama 3.1 8B. This is the first application of patterning, a program grounded in singular learning theory, beyond small models and synthetic tasks.

cs.LG↗
arXiv2026

Skill-as-Pseudocode: Refactoring Skill Libraries to Pseudocode for LLM Agents

Markdown skill libraries for LLM agents ship as free-form prose, forcing the agent to re-derive both the input schema and the concrete invocation syntax on every retrieval. This produces a "confused $\to$ re-retrieve $\to$ still confused" loop: the agent issues a partially-correct action, receives uninformative feedback, and re-retrieves the same prose. We propose Skill-as-Pseudocode (SaP), an automatic conversion of markdown skill libraries into typed pseudocode with deterministic quality control. From each cluster of similar procedural passages, SaP extracts a typed contract and filters it through a four-check deterministic verifier (coverage, binding, replacement, risk). Promoted contracts are inlined into a rewritten skill skeleton alongside restored action templates, giving the agent two complementary signals: a typed signature for what a skill does and a concrete template for how to invoke it. On the ALFWorld unseen split (134 games, gpt-4o-mini, three seeds), SaP wins 82/402 paired games versus 47/402 for the Graph-of-Skills (GoS) baseline (pooled McNemar $p = 8.2 \times 10^{-5}$), at $-22.8 \pm 6.4$% input tokens and $-14.5 \pm 4.1$% LLM calls per game. A bundle-component ablation attributes the gain to the pairing of typed contracts with concrete action templates: the contract alone falls below the prose baseline.

cs.PL↗
arXiv2026

Predicting Spatiotemporal Mobile Sensing-Based PM2.5 Concentrations Using Low-Rank Adapted Spatially Attentive Graph Neural Network

Urban air quality can vary significantly along transit corridors, necessitating high-resolution monitoring. This work introduces a novel mobile-sensing dataset from Surat, Gujarat, India, comprising PM$*{2.5}$ concentrations, meteorological variables (temperature, humidity, wind speed, wind direction), and land-use features. To represent the spatiotemporal data as a graph, two node-definition strategies were used: (i) uniform segmentation (200--400~m intervals) and (ii) DBSCAN clustering to adaptively group dense observations. For each node, rolling mean and standard deviation of meteorological variables were computed. To model this high-dimensional data, we propose a SA-GNN for fine-grained, short-term PM$*{2.5}$ forecasting and hotspot identification. We compared SA-GNN with LSTM, RNN, GRU, and ANN models. These models performed well on low-resolution data but had difficulty capturing rapidly changing patterns in urban air quality. SA-GNN employs cluster-specific GRUs to capture localized temporal dependencies and a Graph Attention Network to learn spatial heterogeneity. This hybrid architecture effectively models rapid fluctuations and complex spatial interactions. On our dataset, SA-GNN achieved $R^2 = 0.95$, RMSE $= 6.8$, and MAE $= 4.2~\si{\micro\gram\per\meter\cubed}$, outperforming all baseline models. Combining spatial clustering with adaptive attention significantly improves forecasting, enabling real-time, fine-grained monitoring and supporting personalized exposure tracking and timely alerts for healthier cities.

cs.AI↗
arXiv2026

MarUco: A Markerless 6D Pose Estimation Framework for Closed-Loop Control of Surgical Continuum Manipulators

Flexible endoscopic continuum manipulators offer high dexterity and access to complex anatomy, but nonlinear hysteresis limits feedforward control accuracy. Closed-loop control can compensate for these errors but requires accurate six-degree-of-freedom (6D) end-effector pose feedback. We present MarUco, a markerless 6D pose estimation framework for closed-loop control using only stereo vision during operation. A photorealistic pseudo-rigid-body simulation pipeline generates large-scale annotated training data without manual labeling. A multifeature fusion network integrates masks, keypoints, heatmaps, and bounding boxes from both stereo views to estimate an initial pose, followed by a learned single-pass render-and-compare module that refines the pose without iterative optimization. Kinematics-free hand-eye calibration estimates camera-to-robot-base extrinsics, and self-supervised adaptation uses unlabeled real stereo pairs to mitigate sim-to-real pose error. Across 1,000 real samples, MarUco achieves translation and rotation errors of 0.78 $\pm$ 0.50 mm and 3.07 $\pm$ 1.25°, respectively, with a total processing time of 52.4 ms per stereo pair. In closed-loop experiments over eight reference paths, MarUco achieves a mean terminal translation error of 1.8 mm, an 88% reduction relative to uncompensated open-loop control. To the best of our knowledge, this is the first markerless position-based visual servoing framework for continuum manipulators.

cs.RO↗
arXiv2026

The half-rate linear programming bound for binary codes is $\frac12-\frac1π$

In their work on sphere packing and the conformal bootstrap, Afkhami-Jeddi, Cohn, Hartman, de Laat, and Tajdini conjectured the exact high-dimensional exponent of the Cohn--Elkies sphere-packing linear program. OpenAI's Chapter 1 subsequently proved their conjecture by establishing that both Fourier sign-uncertainty radii are $(1/π+o(1))\sqrt d$. We prove the binary coding analogue: the half-rate point of the asymptotic binary Delsarte linear program is $1/2-1/π$; equivalently, \[ R_D\!\left(\frac12-\frac1π\right)=\frac12. \] We also formulate the two Krawtchouk sign-uncertainty problems and determine both of their asymptotics. If $A^{\mathrm K}_{\pm}(n)$ denotes the first radial layer after which an origin-vanishing Krawtchouk $(\pm1)$-eigenfunction can be nonnegative, then \[ \frac{A^{\mathrm K}_{\pm}(n)}n\longrightarrow \frac12-\frac1π. \] The common lower bound is the Hamming space counterpart of the mass-concentration principle in the Chapter 1 proof. The upper bound has a different source. It is the binary-code counterpart of the final spherical-code construction in OpenAI's Chapter 2. Gay, Jeronimo, and Liu improved the resulting binary bound and suggested the functional $Φ$ used here, but explicitly evaluated only a few low levels of the corresponding hierarchy. We construct and evaluate compatible binary certificates at every level, attaining the upper bound in the limit. The construction uses an $N$-qubit generalization of the pure-state channel of Alrabiah and Guruswami.

math.CO↗
arXiv2026

Constructions of complete permutations over $\mathbb{F}_q^n$

Complete permutation polynomials play an important role in cryptography, particularly in the design of cryptographic primitives such as the Lai--Massey scheme and S-boxes. We generalize a result of Sun, Li, Guo, and Qu (2021) by characterizing the complete permutation behavior of the mapping $Ψ(X)=M(X+ψ(AX))$ over $\mathbb{F}_q^n$, where $\mathbb{F}_q$ is a finite field of $q$ elements with $q$ being a prime power, $M\in GL(n, \mathbb{F}_q)$, $GL(n, \mathbb{F}_q)$ is the general linear group of order $n$ over $\mathbb{F}_q$, $A_{m \times n}$ is a full-rank matrix over $\mathbb{F}_q$, and $ψ=(ψ_1,ψ_2,\ldots,ψ_n)$ with each component function $ψ_i:\mathbb{F}_q^m\to\mathbb{F}_q$. Furthermore, we establish criteria for the permutation and complete permutation properties of the mapping $F(X)=T(X+B^tf(AX))$ over $\mathbb{F}_{q}^n$, $f: \mathbb{F}_{q}^{m} \rightarrow \mathbb{F}_{q}^{n-m}$, $T \in GL(n, \mathbb{F}_q)$, $A_{m \times n}$ and $B_{(n-m)\times n}$ are full-rank matrices over $\mathbb{F}_q$, $B^t$ represents the transpose of the matrix $B$, and $0<m<n$ are integers. These results also generalize an earlier result of Gravel and Panario (2023), who showed that any arbitrary function $f$ from $\mathbb{F}_q^m$ to $\mathbb{F}_q^{\,n-m}$ can be extended to a bijection over $\mathbb{F}_{q}^n$ through the mapping $F(X)=T(X+B^tf(AX))$, under the condition $AB^t=0$. Here we do not impose the restriction that $AB^t=0$.

cs.CR↗
arXiv2026

Asymptotically Optimal List Size of Random Linear Codes

We prove that for every fixed prime power $q$, every $p\in(0,1-1/q)$, and every $\varepsilon>0$ with $1-H_q(p)-\varepsilon>0$, a random linear code over $\mathbb{F}_q$ of rate $1-H_q(p)-\varepsilon$ is $(p,\,\left\lceil\frac{H_q(p)}{\varepsilon}\right\rceil+O_{p,q}(1))\text{-list-decodable}$ with probability at least $1-q^{-Ω(n)}$. Guruswami, Li, Mosheiff, Resch, Silas, and Wootters showed that, for sufficiently small $\varepsilon$, random linear codes require list size at least $\left\lfloor\frac{H_q(p)}{\varepsilon}+0.99\right\rfloor,$ and conjectured that $\frac{H_q(p)}{\varepsilon}(1+o(1))$ suffices as $\varepsilon\to 0$. This conjecture was previously known for $q=2$, where the upper bound $H_2(p)/\varepsilon+2$ was established. For $q>2$, however, the best known upper bound was $C_{p,q}/\varepsilon$ for a constant $C_{p,q}$ depending on $p$ and $q$. Our result resolves the conjecture for every prime power $q$ and, in fact, establishes the sharper upper bound $\frac{H_q(p)}{\varepsilon}+O_{p,q}(1)$.

cs.IT↗