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arXiv · 2610.08610

Reed-Solomon Codes at Capacity: Algorithmic List-Decoding and Proximity Gaps

Prahladh Harsha·Mrinal Kumar·Ramprasad Saptharishi
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Abstract

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.

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Prahladh Harsha, Mrinal Kumar, Ramprasad Saptharishi. 2026-10-06. Reed-Solomon Codes at Capacity: Algorithmic List-Decoding and Proximity Gaps. https://arxiv.org/abs/2610.08610

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