Distance sets of two subsets of vector spaces over finite fields
  We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of the two subsets. As a result, we improve upon the results by Rainer Dietmann. In the case that one of the subsets is a product set, we obtain further improvement on the estimate. 
Doowon Koh and Hae-Sang Sun
math.CO