发表机构
Tata Institute of Fundamental Research（塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文统一阐述了 Reed-Solomon 码在容量极限下的算法列表解码及邻近间隙问题的突破性结果，并提供了清晰完整的证明概述。
AI 中文摘要
理解 Reed-Solomon 码的列表可解码性极限一直是代数编码理论中最重要的开放问题之一。最近，Brakensiek、Chen、Putterman、Zhang 和 Zheng 取得了重大突破，证明了大特征域上的 Reed-Solomon (RS) 码在算法上可列表解码直至容量极限。基于这一结果，Jeronimo 随后扩展了这些技术，解决了 RS 码的邻近间隙问题。在本文中，我们对这些结果给出了统一且清晰的阐述。
英文摘要
Understanding the limits of list-decodability of Reed-Solomon codes has been one of the most important open problems in algebraic coding theory. Recently, Brakensiek, Chen, Putterman, Zhang, and Zheng, in a remarkable breakthrough, showed that Reed-Solomon (RS) codes over fields of large characteristic are algorithmically list-decodable all the way up to capacity. Building on this result, Jeronimo subsequently extended these techniques to solve the proximity-gaps question for RS codes. In this article, we give a unified and transparent exposition of these results.
