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On the list recoverability of randomly punctured codes (2005.02478v3)
Published 4 May 2020 in math.CO, cs.CC, cs.DM, cs.IT, and math.IT
Abstract: 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.