Definition:Block Incidence Matrix of a Design

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

$a_{ij}=\begin{cases} 1 & : \text{ if the } i^{th} \text { point is in the } j^{th} \text { block} \\ 0 & : \text{ otherwise} \end{cases}$