Algorithmizing the recent combinatorial list-size bounds for FRS list decoding

Develop an efficient algorithm—ideally running in time nearly linear in the code length or at least polynomial in the output list size—that, given a received word for a Folded Reed–Solomon (FRS) code, outputs all codewords within Hamming radius 1 − R − ε, thereby algorithmizing the improved combinatorial list-size bounds achieved by Srivastava (O(1/ε^2)) and by Chen–Zhang (O(1/ε)).

Background

Folded Reed–Solomon (FRS) codes achieve list-decoding capacity, and earlier algorithmic analyses (e.g., Kopparty–Ron-Zewi–Saraf–Wootters and Tamo) provided explicit procedures but with list-size bounds of the form (1/ε)^{O(1/ε)}. Very recent works by Srivastava and by Chen–Zhang improved the combinatorial list-size bounds to O(1/ε^2) and O(1/ε), respectively, essentially matching the generalized Singleton bound up to constants.

However, these new proofs are combinatorial and do not yield efficient decoding algorithms. The paper explicitly notes that turning these bounds into efficient algorithms—ideally with running time nearly linear in the code length n or even just polynomial in the list size—remains open. This problem asks for such an algorithmic development that matches the improved bounds while maintaining practical computational complexity.