# Punctured Large Distance Codes, and Many Reed-Solomon Codes, Achieve List-Decoding Capacity

@article{Guruswami2021PuncturedLD, title={Punctured Large Distance Codes, and Many Reed-Solomon Codes, Achieve List-Decoding Capacity}, author={Venkatesan Guruswami and Jonathan Mosheiff}, journal={Electron. Colloquium Comput. Complex.}, year={2021}, volume={28}, pages={139} }

We prove the existence of Reed-Solomon codes of any desired rate R ∈ (0, 1) that are combinatorially list-decodable up to a radius approaching 1 − R, which is the informationtheoretic limit. This is established by starting with the full-length [q, k]q Reed-Solomon code over a field Fq that is polynomially larger than the desired dimension k, and “puncturing” it by including k/R randomly chosen codeword positions. Our puncturing result is more general and applies to any code with large minimum… Expand

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