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Representative Papers

On the Algebraic Structure Underlying the Support Enumerators of Linear Codes

Jan 13, 2026

This work addresses the limitation of classical weight distributions in linear codes, which fail to capture coordinate-wise nonzero activity with sufficient granularity. To overcome this, the paper introduces, for the first time, the notions of support distribution and support enumerator, refining the traditional weight distribution to enable a coordinate-level characterization of nonzero symbol occurrences. The authors establish explicit counting formulas for such coordinate-wise activity and derive a MacWilliams-type identity relating the support enumerators of a linear code and its dual. Building on this framework, they formulate an algebraic duality relation for support enumerators and provide a novel criterion for self-dual codes based on the equality of their support distributions. This contribution deepens the structural understanding of linear codes, enriches duality theory at the coordinate level, and offers a new tool for constructing and identifying self-dual codes.

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A Concise Review of Hallucinations in LLMs and their Mitigation

Dec 02, 2025

This paper systematically surveys hallucination in large language models (LLMs), clarifying its root causes—including training data bias, decoding-induced distortion, and incomplete knowledge representation—and classifying its multidimensional manifestations (e.g., factual, logical, and consistency hallucinations). Methodologically, it proposes a unified hallucination taxonomy and establishes a three-layer mitigation framework—detection, attribution, and suppression—that integrates major technical paradigms: pretraining interventions, prompt engineering, retrieval-augmented generation, and post-hoc correction. Through structured literature analysis and mechanistic dissection of representative approaches, the work delivers the first practice-oriented, one-stop knowledge portal for hallucination governance. The resulting concise survey document enhances research reproducibility and accelerates real-world deployment, providing both theoretical foundations and methodological guidance for advancing LLM trustworthiness.

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Latest Papers

On the Algebraic Structure Underlying the Support Enumerators of Linear Codes

Jan 13, 2026

This work addresses the limitation of classical weight distributions in linear codes, which fail to capture coordinate-wise nonzero activity with sufficient granularity. To overcome this, the paper introduces, for the first time, the notions of support distribution and support enumerator, refining the traditional weight distribution to enable a coordinate-level characterization of nonzero symbol occurrences. The authors establish explicit counting formulas for such coordinate-wise activity and derive a MacWilliams-type identity relating the support enumerators of a linear code and its dual. Building on this framework, they formulate an algebraic duality relation for support enumerators and provide a novel criterion for self-dual codes based on the equality of their support distributions. This contribution deepens the structural understanding of linear codes, enriches duality theory at the coordinate level, and offers a new tool for constructing and identifying self-dual codes.

0 citationsRead paper

A Concise Review of Hallucinations in LLMs and their Mitigation

Dec 02, 2025

This paper systematically surveys hallucination in large language models (LLMs), clarifying its root causes—including training data bias, decoding-induced distortion, and incomplete knowledge representation—and classifying its multidimensional manifestations (e.g., factual, logical, and consistency hallucinations). Methodologically, it proposes a unified hallucination taxonomy and establishes a three-layer mitigation framework—detection, attribution, and suppression—that integrates major technical paradigms: pretraining interventions, prompt engineering, retrieval-augmented generation, and post-hoc correction. Through structured literature analysis and mechanistic dissection of representative approaches, the work delivers the first practice-oriented, one-stop knowledge portal for hallucination governance. The resulting concise survey document enhances research reproducibility and accelerates real-world deployment, providing both theoretical foundations and methodological guidance for advancing LLM trustworthiness.

0 citationsRead paper