On the values of Kloosterman sums

Igor E. Shparlinski

doi:10.1109/TIT.2009.2018320

On the values of Kloosterman sums

Igor E. Shparlinski^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

73 Downloads (Pure)

Abstract

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

Original language	English
Pages (from-to)	2599-2601
Number of pages	3
Journal	IEEE Transactions on Information Theory
Volume	55
Issue number	6
DOIs	https://doi.org/10.1109/TIT.2009.2018320
Publication status	Published - 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 Universityâ€™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 [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

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On the values of Kloosterman sums

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