List-decoding and list-recovery of Reed-Solomon codes beyond the Johnson radius for any rate
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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 of attention in recent decades. However, the best possible parameters for these problems are still unknown, and in this paper, we take a step in this direction. We show the existence of RS codes that are list-decodable or list-recoverable beyond the Johnson radius for any rate, with a polynomial field size in the block length. In particular, we show that for any ϵ∈ (0,1) there exist RS codes that are list-decodable from radius 1-ϵ and rate less than ϵ/2-ϵ, with constant list size. We deduce our results by extending and strengthening a recent result of Ferber, Kwan, and Sauermann on puncturing codes with large minimum distance and by utilizing the underlying code's linearity.
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