3 problems

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 $s$,

Let $r$ be a positive integer, and let the $[2^r-1,r]$ simplex code be the binary simplex code of length $2^r-1$ and dimension $r$. Let $FB(r,k)$ denote the minimum number of serve…