Distance sets of two subsets of vector spaces over finite fields

Doowon Koh, Hae-Sang Sun

Published 2012-12-21, updated 2013-04-19Version 2

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.