International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 59482, 5 pages
doi:10.1155/IJMMS/2006/59482
On the set of distances between two sets over finite fields
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
Received 13 March 2006; Revised 12 May 2006; Accepted 9 July 2006
Copyright © 2006 Igor E. Shparlinski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.