Definition:Block Incidence Matrix of a Design

The block incidence matrix of a $$(v,b,r,k,\lambda)$$-BIBD, is a $$v\times b$$ matrix $$A=(a_{ij})$$ such that:

$$a_{ij}=\begin{cases} 1 \mbox{ if the }i^{th}\mbox{ point is in the } j^{th} \mbox{ block, and}\\ 0 \mbox{ otherwise}\\ \end{cases}$$