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Designs, Codes and Cryptography

, Volume 49, Issue 1–3, pp 347–357 | Cite as

On binary Kloosterman sums divisible by 3

Article

Abstract

By counting the coset leaders for cosets of weight 3 of the Melas code we give a new proof for the characterization of Kloosterman sums divisible by 3 for \({\mathbb{F}_{2^m}}\) where m is odd. New results due to Charpin, Helleseth and Zinoviev then provide a connection to a characterization of all \({a\in\mathbb{F}_{2^m}}\) such that \({Tr(a^{1/3})=0}\); we prove a generalization to the case \({Tr(a^{1/(2^k-1)})=0}\). We present an application to constructing caps in PG(n, 2) with many free pairs of points.

Keywords

Binary Kloosterman sum Melas code Nonlinear function Cap 

AMS Classifications

11T71 11L05 94B15 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada

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