2 problems

Functional Batch Conjecture. The binary $[k,2^k-1]$ simplex code is a $2^{k-1}$-functional batch code.

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…