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On the Values of Kloosterman Sums

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1 Author(s)
Shparlinski, I.E. ; Dept. of Comput., Macquarie Univ., Sydney, NSW

Given a prime p and a positive integer n, we show that the shifted Kloosterman sums SigmaxisinF p nPsi(x + alphaxpn-2)=SigmaxisinF* p nPsi(x+alphax-1)+1, alphaisinF*pn where Psi is a nontrivial additive character of a finite field Fpn of pn elements, do not vanish if alpha 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.

Published in:

Information Theory, IEEE Transactions on  (Volume:55 ,  Issue: 6 )

Date of Publication:

June 2009

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