On the set of distances between two sets over finite fields
We use bounds of exponential sums to derive new lower bounds on the number of distinct distances between all pairs of points (x,y)∈×ℬ for two given sets ,ℬ∈Fqn, where Fq is a finite field of q elements and n≥1 is an integer.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/59482 |
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| _version_ | 1849764911013429248 |
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| author | Igor E. Shparlinski |
| author_facet | Igor E. Shparlinski |
| author_sort | Igor E. Shparlinski |
| collection | DOAJ |
| description | We use bounds of exponential sums to derive new lower bounds on the number of distinct distances between all pairs of points (x,y)∈×ℬ for two given sets ,ℬ∈Fqn, where Fq is a finite field of q elements and n≥1 is an integer. |
| format | Article |
| id | doaj-art-ce1cc8816bac475ebf2cfbd2ccfd174b |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ce1cc8816bac475ebf2cfbd2ccfd174b2025-08-20T03:05:01ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/5948259482On the set of distances between two sets over finite fieldsIgor E. Shparlinski0Department of Computing, Macquarie University, Sydney, NSW 2109, AustraliaWe use bounds of exponential sums to derive new lower bounds on the number of distinct distances between all pairs of points (x,y)∈×ℬ for two given sets ,ℬ∈Fqn, where Fq is a finite field of q elements and n≥1 is an integer.http://dx.doi.org/10.1155/IJMMS/2006/59482 |
| spellingShingle | Igor E. Shparlinski On the set of distances between two sets over finite fields International Journal of Mathematics and Mathematical Sciences |
| title | On the set of distances between two sets over finite fields |
| title_full | On the set of distances between two sets over finite fields |
| title_fullStr | On the set of distances between two sets over finite fields |
| title_full_unstemmed | On the set of distances between two sets over finite fields |
| title_short | On the set of distances between two sets over finite fields |
| title_sort | on the set of distances between two sets over finite fields |
| url | http://dx.doi.org/10.1155/IJMMS/2006/59482 |
| work_keys_str_mv | AT igoreshparlinski onthesetofdistancesbetweentwosetsoverfinitefields |