2 problems

Let $H_q^n$ be the Hamming space over an alphabet of size $q$, and let $C\subseteq H_q^n$ be an equidistant code with distance $d$. Hegedüs' conjecture. If … then … This conjecture…

Optimality conjecture. There exists a constant $s_q$ such that whenever $s\in[-1,s_q)\cap T_n$, the refinements described above are the best bounds that can be obtained from Theore…