Designs, Codes and Cryptography

, Volume 49, Issue 1, pp 347–357

On binary Kloosterman sums divisible by 3

Article

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

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 

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada

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