TY - JOUR
T1 - On the values of Kloosterman sums
AU - Shparlinski, Igor E.
N1 - 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.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=66949160797&partnerID=8YFLogxK
U2 - 10.1109/TIT.2009.2018320
DO - 10.1109/TIT.2009.2018320
M3 - Article
AN - SCOPUS:66949160797
VL - 55
SP - 2599
EP - 2601
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 6
ER -