List-Decoding and List-Recovery of Reed-Solomon Codes Beyond the Johnson Radius for Every Rate

Eitan Goldberg, Chong Shangguan*, Itzhak Tamo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 every rate, with a polynomial field size in the block length. In particular, we show that for every 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.

Original languageEnglish
Pages (from-to)2261-2268
Number of pages8
JournalIEEE Transactions on Information Theory
Volume69
Issue number4
DOIs
StatePublished - 1 Apr 2023

Funding

FundersFunder number
European Research Council852953
National Natural Science Foundation of China12101364, 12231014
Israel Science Foundation1030/15
Natural Science Foundation of Shandong ProvinceZR2021QA005
National Key Research and Development Program of China2021YFA1001000

    Keywords

    • Johnson radius
    • List-decoding
    • list-recovery
    • reed-solomon codes

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