There Exist Caps Which Block All Spaces of Fixed Codimension in G (n, 2)

Recall that a cap in PG(n, 2) is simply a set of points with no three collinear. A cap which intersected all codimension 2 subspaces would yield an interesting example of a 2-block: 2-blocks have been much studied in the literature. An interesting folklore conjecture, which received considerable attention, had it that in fact no cap is a 2-block. Although this conjecture can be shown to be true for small dimensions, we show that is far from being the case in general. Article No. 0010