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Understanding the limits of list-decoding and list-recovery of Reed-Solomon(RS) codes is of prime interest in coding theory and has attracted a lot ofattention in recent decades. However, the best possible parameters for theseproblems are still unknown, and in this paper, we take a step in thisdirection. We show the existence of RS codes that are list-decodable orlist-recoverable beyond the Johnson radius for \emph{any} rate, with apolynomial field size in the block length. In particular, we show that for any$\epsilon\in (0,1)$ there exist RS codes that are list-decodable from radius$1-\epsilon$ and rate less than $\frac{\epsilon}{2-\epsilon}$, with constantlist size. We deduce our results by extending and strengthening a recent resultof Ferber, Kwan, and Sauermann on puncturing codes with large minimum distanceand by utilizing the underlying code's linearity.

List-decoding and list-recovery of Reed-Solomon codes beyond the Johnson radius for any rate