2 problems

Cyclicity conjecture for Abelian planar difference sets. The period of $\mathcal L$ in $A_n$ along $\mathbf f_{i,j}$ is equal to $n^2+n+1$ for at least one vector $\mathbf f_{i,j}$…

Prime power conjecture. There exists a linear $1$-perfect code in $(A_n,d)$, equivalently in $(\mathbb{Z}^n,d_a)$, if and only if $n$ is a prime power.