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On the list recoverability of randomly punctured codes

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arxiv 2005.02478 v3 pith:W4SUAPVD submitted 2020-05-04 math.CO cs.CCcs.DMcs.ITmath.IT

Ben Lund , Aditya Potukuchi This is my paper · ORCID
classification math.COcs.CCcs.DMcs.ITmath.IT
keywords codeslistreed-solomonbeyondboundjohnsonrecoverablethere
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We show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound. In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound. It was previously known that there are Reed-Solomon codes that do not have this property. As an immediate corollary to our main theorem, we obtain better degree bounds on unbalanced expanders that come from Reed-Solomon codes.

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  1. Decoding Insertions/Deletions via List Recovery

    cs.IT 2025-05 conditional novelty 6.0 of 10

    Any (ρ, 2ρn+1, L)-list-recoverable code is a (ρ, L)-list-decodable insdel code, yielding the first polynomial-time insdel decoder for [n,k] Reed-Solomon codes with k > 2.

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