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Abstract

We prove that folded Reed–Solomon codes with primitive-power evaluation blocks and two allowed symbols at each coordinate have output list size at most seven at every asymptotic rate R<2/3-8ρ/9, where 0≤ρ<3/4 is the disagreement fraction. The result holds in the stronger average-radius sense, with explicit finite-parameter folding and field-size conditions. The proof assigns one nonnegative subspace certificate to each configuration of eight messages, controlling the two largest fibers of every linear quotient, including partial captures. Every eight-point configuration over any field has certificate cost at most nine, and the Boolean three-cube attains nine. Combining this inequality with classical folded-Wronskian rank bounds gives the input-two, output-seven case of the Chen–Zhang tradeoff. Retaining partial-overlap windows in the folded determinant gives a quadratic intersection budget and sharper integer finite-folding profiles. These certify, for example, n=10, k=120 and ρ=1/4 at folding 29 over F₅₁₂. The same certificate applies to multiplicity codes in characteristic at least k; its derivative-Wronskian ramification budget certifies folding 28 over F₃₃₁ for the same n,k,ρ. Binary input refers to the two allowed symbols, independently of the field characteristic.