4 problems

Generalized-polygon pseudocodeword-weight conjecture. We conjecture that incidence graphs of generalized $N$-gons yield LDPC codes with $w_{\min}$ very close to $d_{\min}$ and, par…

Let $q>4$ be a prime power, and let $\mathrm{H}(q)$ be the split Cayley generalized hexagon of order $q$, with dual $\mathrm{H}(q)^D$. A generalized hexagon is semi-finite if it ha…

Let $s\ge 2$ and $n\ge 3$, and let $\mathcal{G}=({{\mathcal P}},{{\mathcal L}};{\mathcal I})$ be a generalized $n$-gon of order $s$, so its Levi graph is $(s+1)$-regular, has diame…

Affine-building characterization conjecture. $\Gamma$ is “isomorphic” to the building at infinity of some thick affine building of type $\widetilde{\mathsf{G}}_2$ if and only if th…