Designs, Codes and Cryptography

, Volume 49, Issue 1, pp 347–357

On binary Kloosterman sums divisible by 3


DOI: 10.1007/s10623-008-9171-0

Cite this article as:
Garaschuk, K. & Lisoněk, P. Des. Codes Cryptogr. (2008) 49: 347. doi:10.1007/s10623-008-9171-0


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.


Binary Kloosterman sum Melas code Nonlinear function Cap 

AMS Classifications

11T71 11L05 94B15 

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada

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