Symmetric $(15,8,4)$-designs in terms of the geometry of binary simplex codes of dimension $4$

Mark Pankov, Krzysztof Petelczyc, Mariusz Żynel

Let $n=2^k-1$ and $m=2^{k-2}$ for a certain $k\ge 3$. Consider the point-line geometry of $2m$-element subsets of an $n$-element set. Maximal singular subspaces of this geometry co…