  A novel lower bound is introduced for the full rank probability of random
finite field matrices, where a number of elements with known location are
identically zero, and remaining elements are chosen independently of each
other, uniformly over the field. The main ingredient is a result showing that
constraining additional elements to be zero cannot result in a higher
probability of full rank. The bound then follows by "zeroing" elements to
produce a block-diagonal matrix, whose full rank probability can be computed
exactly. The bound is shown to be at least as tight and can be strictly tighter
than existing bounds.
