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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 14, Article ID 59482, 5 pages
doi:10.1155/IJMMS/2006/59482

On the set of distances between two sets over finite fields

Igor E. Shparlinski

Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

Abstract

We use bounds of exponential sums to derive new lower bounds on the number of distinct distances between all pairs of points (x,y)∈𝒜×ℬ for two given sets 𝒜,ℬ∈Fqn, where Fq is a finite field of q elements and n≥1 is an integer.