4 problems

Low-dimensional sum-set decomposition conjecture. For every choice of $\ell\in\mathbb N$, $\varepsilon>0$, and $R>0$, the decomposition above exists for all sufficiently large fold…

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 s…

LMS conjecture. The lower bound $L\geq \ell^{\Omega(1/\eps)}$ applies to all linear codes achieving the Elias Bound for List Recovery.

Reed–Solomon list-recoverability conjecture. The number of polynomials $P(X) \in \mathbb{F}_p[X]$ satisfying