4 problems

Let $r_F(n;s,t)$ denote the minimum redundancy of a binary functional $(s,t)$-batch code encoding $n$ information symbols. For $1\leqslant s\leqslant t\leqslant 2^n-1$, write…

Fix $s\geqslant 2$. An $FB(s,k)$ functional batch code is a binary-server scheme storing linear combinations of $s$ information symbols such that every multiset of $k$ linear reque…

Let $ASP(k,t,q)$ and $ASB(k,t,q)$ denote the minimum lengths of, respectively, all-symbol PIR and all-symbol batch codes with parameters $k,t,q$. For all $k,q$ and $t_1,t_2\geq 1$,…

Optimal functional $2^{s-1}$-batch code conjecture. For any $s$,