Chen–Zhang's optimal list-recovery conjecture for folded Reed–Solomon codes

Let $\theta=\frac{L+1-\beta}{L+1}$ denote the list-recovery agreement parameter, and let $\rho^*$ be defined by

$$\rho^*=\frac{L+1-\ell}{L+1}\left(1-\frac{aR}{a-1}\right).$$

For constants $\epsilon>0$, $ell\rm oindent\ge 2$, $L+1=\ell^a$ with $a\in\mathbb{N}^{\ge 2}$, $R\leq\frac{a-1}{a}$, and a generator $gamma$ of $\mathbb{F}^{\times}_q$, there is a constant $C$ such that, whenever $s\ge C$, $(k-1)/s\ge a$, and $n$ is sufficiently large, every rate-$R$ folded Reed–Solomon code

$$\mathsf{FRS}^{s,\gamma}_{n,k}(\alpha_1,\alpha_2,\dots,\alpha_n)$$

with appropriate evaluation points in $\mathbb{F}_q$ is $(\rho^*-\varepsilon,\ell,L)$ list-recoverable.

Chen–Zhang's conjecture. For the stated parameters, folded Reed–Solomon codes achieve list-recovery radius arbitrarily close to $\rho^*$ with input list size $ell$ and output list size $L$. The conjecture predicts the optimal tradeoff for these structured codes; its status is not resolved in the supplied source.