We provide a deterministic polynomial-time list decoding algorithm for Reed–Solomon codes over prime fields that approaches list decoding capacity on every evaluation set for any (constant) rate.

This revision boosts our main result from low rates to all constant rates, thanks to a neat observation by Omar Alrabiah, Rohan Goyal, and Venkat Guruswami.

We provide a deterministic polynomial-time list decoding algorithm for Reed-Solomon codes over prime fields that approaches list decoding capacity on every evaluation set in the low (constant) rate regime.