A transform property of Kloosterman sums

Authors:
Ian F. Blake;Theo Garefalakis
Affiliations:
Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada;Department of Mathematics, University of Crete, 71409 Heraklion, Greece
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

An expression for the number of times a certain trace function associated with a Kloosterman sum on an extension field assumes a given value in the base field is given and its properties explored. The relationship of this result to the enumeration of certain types of irreducible polynomials over fields of characteristic two or three and to the weights in the dual of a Melas code is considered. It is argued that the expressions obtained for the trace functions, while simply related to the Kloosterman sums, can be more directly useful than the exponential sums themselves in certain applications. In addition, they enjoy properties that are of independent interest.