Distance sets of two subsets of vector spaces over finite fields

Koh, Doowon; Sun, Hae-Sang

doi:10.1090/S0002-9939-2014-12386-0

Distance sets of two subsets of vector spaces over finite fields
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by Doowon Koh and Hae-Sang Sun PDF

Proc. Amer. Math. Soc. 143 (2015), 1679-1692 Request permission

Abstract:

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.

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