%0 Journal Article
%T On the rank of random matrices over finite fields
%A Daniel Salmond
%A Alex Grant
%A Ian Grivell
%A Terence Chan
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1404.3250v1