List-size conjecture for Reed–Solomon codes beyond the Johnson radius
List-size conjecture for Reed–Solomon codes beyond the Johnson radius
For a code of rate over a finite field, list-decodable from relative radius with list size means that every Hamming ball of radius contains at most codewords. List-size conjecture beyond the Johnson radius. For any , there exist Reed–Solomon codes with rate over a sufficiently large finite field that are list-decodable from radius with list size at most . This gives an explicit target for the list size as the decoding radius approaches the rate-one capacity threshold; the source presents it as implied by the preceding conjecture and does not report a proof or disproof.
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Sources & referencesView supporting material
Primary source
Chong Shangguan and Itzhak Tamo, “Combinatorial list-decoding of Reed-Solomon codes beyond the Johnson radius”, arXiv:1911.01502 (2019).
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