4 problems

Let $d$ be fixed, and consider the degree-$d$ Reed–Solomon code with evaluation set $FbbF_q$. A random puncturing is obtained by retaining a random subset of evaluation coordinates…

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…

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