The paper proves that random Reed-Solomon (RS) codes are list recoverable up to capacity with optimal output list size, for any input list size. Specifically:
For any positive integers n, ℓ, any small enough ε > 0, and any rate R ∈ (0, 1-ε), the authors show that a random RS code RS(α1, ..., αn; Rn) is (1-R-ε, ℓ, L=O(ℓ/ε)) list recoverable with high probability, over a finite field Fq with q ≥ ℓᶿ(ℓ²/Rε³) · n².
This result improves upon previous work in several aspects:
The proof builds upon and extends the recent techniques for list decoding of random RS codes, introducing the notion of an "extended reduced intersection matrix" to handle the list recovery setting.
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by Dean Doron,S... at arxiv.org 04-02-2024
https://arxiv.org/pdf/2404.00206.pdfDeeper Inquiries