On binary Kloosterman sums divisible by 3 |
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Authors: | Kseniya Garaschuk Petr Lisoněk |
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Institution: | 1. Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada, V5A 1S6
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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. |
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