For finite-field Reed--Solomon codes operatornameRS_q[n,k]=(f(a))_a∈ A:f∈F_q[X], deg f<k, determine the exact finite parameter region, and in particular the largest relative radius delta, for which the code satisfies the mutual correlated agreement (MCA) property. The problem includes the constant-relative regime between the Johnson radius and the list-decoding-capacity radius 1-k/n.

Reed–Solomon mutual correlated agreement problem

The problem asks how far mutual agreement can be guaranteed for Reed–Solomon codes, especially between the Johnson regime and list-decoding capacity. Public work now gives partial bounds and structural reductions, but no complete finite or constant-relative solution.

Known results

The WHIR result proves MCA in the unique-decoding range, $\delta < (1-\rho)/2$ .
An ACFY25 conjecture for univariate power generators is reported resolved through the Johnson regime, under $\gamma \le 1-(1+1/(2m))\sqrt{\rho}$ .
Ben-Sasson, Carmon, Haböck, Kopparty, and Saraf, independently Crites and Stewart, relate sufficiently strong MCA to Reed–Solomon list-decodability with a shifted degree parameter.

July–August 2026 bounds and conjectures

A July preprint derives MCA lower bounds from list-decoding counterexamples and specializes them to Reed–Solomon codes, without resolving the problem. A 2026 preprint reports deterministic polynomial control a fixed number of steps beyond Johnson, including certified finite parameters, but leaves constant-relative improvement open. The August framework proposes conjectural profiles for the unresolved finite regime; these conjectures are unproved.

Current status (as of August 2026): Partial bounds and reductions are established, but the finite Reed–Solomon MCA problem beyond the Johnson regime, especially constant-relative improvement toward capacity, remains open.

Reed–Solomon mutual correlated agreement problem

Progress summary

Primary source

Additional references

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