On binary Kloosterman sums divisible by 3

Autor: Kseniya Garaschuk, Petr Lisonĕk
Rok vydání: 2008
Předmět:
Zdroj: Designs, Codes and Cryptography. 49:347-357
ISSN: 1573-7586
0925-1022
DOI: 10.1007/s10623-008-9171-0
Popis: 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.
Databáze: OpenAIRE
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