On certain values of Kloosterman sums

Authors:
Marko J. Moisio
Affiliations:
Department of Mathematics and Statistics, University of Vaasa, Vaasa, Finland
Venue:
IEEE Transactions on Information Theory
Year:
2009

Citing 4
Cited 2

Finite fields

Finite fields
On the values of Kloosterman sums

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Monomial and quadratic bent functions over the finite fields of odd characteristic

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Hyperbent Functions, Kloosterman Sums, and Dickson Polynomials

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On integer values of Kloosterman sums

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On zeros of Kloosterman sums

Designs, Codes and Cryptography

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Abstract

Let Kqn(a) be a Kloosterman sum over the finite field Fqn of characteristic p. In this note so called subfield conjecture is proved: if a ≠ 0 belongs to the proper subfield Fq of Fqn, then Kqn(a) ≠ -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.