On Certain Values of Kloosterman Sums
Marko J. Moisio · IEEE Transactions on Information Theory · 2009
LetKqn(a) be a Kloosterman sum over the finite fieldFqnof characteristicp. In this note so called subfield conjecture is proved: ifane 0 belongs to the proper subfieldFqofFqn, thenKqn(a) ne -1. This completes recent works on the subfield conjecture by Shparlinski, and Moisio and Lisonek. The problem is motivated by some applications to bent functions. Moreover, in the course of the proof a large class of translates of Dickson polynomials are shown to be irreducible.