List-size conjecture for Reed–Solomon codes beyond the Johnson radius

From papers

For a code of rate RR over a finite field, list-decodable from relative radius rr with list size LL means that every Hamming ball of radius rnr n contains at most LL codewords. List-size conjecture beyond the Johnson radius. For any R,ϵ>0R,\epsilon>0, there exist Reed–Solomon codes with rate RR over a sufficiently large finite field that are list-decodable from radius 1Rϵ1-R-\epsilon with list size at most 1Rϵϵ\frac{1-R-\epsilon}{\epsilon}. 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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