On the Compressed Measurements over Finite Fields: Sparse or Dense   Sampling
  We consider compressed sampling over finite fields and investigate the number of compressed measurements needed for successful L0 recovery. Our results are obtained while the sparseness of the sensing matrices as well as the size of the finite fields are varied. One of interesting conclusions includes that unless the signal is "ultra" sparse, the sensing matrices do not have to be dense. 
Jin-Taek Seong and Heung-No Lee
cs.IT math.IT