5 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…

Let $\mathbb{F}^n$ and $\mathbb{F}^m$ be binary Hamming spaces, and let $Id_r(\mathbb{F}^n)$ denote the minimum cardinality of an identifying code of radius $r$ in $\mathbb{F}^n$.…

Let $mathcal{H}q^n$ be the $q$-ary Hamming space, and let $A(mathcal{H}q^n,{2,4})$ denote the maximum size of a code whose occurring nonzero Hamming distances are $2$ and $4$. **B…

Samorodnitsky's conjecture. The McEliece–Rodemich–Rumsey–Welch feasible solution is asymptotically optimal for the dual program in Delsarte's linear programming approach as the blo…

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…