On the values of Kloosterman sums

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
20 Downloads (Pure)


Given a prime p and a positive integer n, we show that the shifted Kloosterman sums ∑χ∈ℱpn ψ(χ + aχpn-2) = ∑χ∈ℱ*pnψ(χ + aχ-1)+1, a ∈ℱ*pn where ψ is a nontrivial additive character of a finite field Fpn of pn elements, do not vanish if a belongs to a small subfield Fpm sube Fpn. This complements recent results of P. Charpin and G. Gong which in turn were motivated by some applications to bent functions.

Original languageEnglish
Pages (from-to)2599-2601
Number of pages3
JournalIEEE Transactions on Information Theory
Issue number6
Publication statusPublished - 2009

Bibliographical note

Copyright 2009 IEEE. Reprinted from IEEE transactions on information theory, Volume 55, Issue 6, 2599-2601. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Macquarie University’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

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