How can I construct sparse binary matrices $A : M \times N$, with ~ $N p$ ones in each row,
so that rows don't overlap much, i.e. the maximum
$\qquad \text{size} (\ A \text{ row } i \ \cap\ A \text{ row } j\ )$
over all pairs of rows is small ? I'm looking for simple code or pseudocode, for small overlap -- not as small as possible. Example sizes: $M = N = 1000000,\ p = 0.001$ .
(Generating a random matrix, then dropping rows with high overlap, might do the job. A systematic construction with some "Coding theory for dummies" would be nice though.)