Where do Bernoulli random matrices arise?

Question

A $n\times m$ matrix $A=(a_{i,j})_{i,j}$ is called Bernoulli random matrix if $\{a_{i,j}\}_{i,j}$ are iid signed Bernoulli rv's, that is $$ P(a_{1,1}=1)=P(a_{1,1}=-1)=\frac{1}{2}. $$ I was wondering in which examples this type of random matrix ensemble is of major importance.