By Topic

On Integer Values of Kloosterman Sums

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Kononen, K.P. ; Dept. of Math. Sci., Univ. of Oulu, Oulun, Finland ; Rinta-aho, M.J. ; Väänänen, K.O.

This paper considers rational integer values of Kloosterman sums over finite fields of characteristic p > 3. We shall prove two main results. The first one is a congruence relation satisfied by possible integer values. One consequence is that there are no Kloosterman zeroes in the case of characteristic p > 3, which generalizes recent works by Shparlinski, Moisio, and Lisoněk on this subject. This, in turn, implies that there are no Dillon type bent functions in the case p > 3 , thus answering a question posed recently by Helleseth and Kholosha. Our other main result states that the Kloosterman sum obtains an integer value at a point if and only if the same sum lifted to any extension field remains an integer.

Published in:

Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 8 )