The divisibility modulo 24 of Kloosterman sums on \(\text{GF}(2^m)\), \(m\) odd
type: Item
instance of: scholarly article
title: The divisibility modulo 24 of Kloosterman sums on \(\text{GF}(2^m)\), \(m\) odd
zbMATH Open document ID: 1112.11055
author: Pascale Charpin
author: Tor Helleseth
author: Victor A. Zinoviev
published in: Journal of Combinatorial Theory. Series A
publication date: 2007-02-26T00:00:00Z
review text: This paper continues previous work by the authors. Here they exploit the connection between binary primitive extended BCH codes of length \(2^m\) (\(m\) odd) with minimal distance 8 and Kloosterman sums over finite fields of order \(2^m\). Some properties on the divisibility of the inverse-cubic sums have been derived. In Theorem 2, the authors state the key congruences which allow computation of the divisibility of Kloosterman sums modulo 24. The results of Theorem 3 provide six different cases which depend each on the form of \(m\). In section 5, the connection between Kloosterman sums and the \([2^m+ 1,2m]\) irreducible code have been recalled and the consequences of the authors' results on the weight distribution of this code have been explained. Finally, the spectrum of Kloosterman sums has been studied.
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 94B25
zbMATH DE Number: 5129735
zbMATH Keywords: BCH codes
zbMATH Keywords: Kloosterman sums
zbMATH Keywords: exponential sums
zbMATH Keywords: Melas code
zbMATH Keywords: cosets
zbMATH Keywords: irreducible code
zbMATH Keywords: divisibility
reviewed by: Bai Kishan Dass
MaRDI profile type: Publication
full work available at URL: j.jcta.2006.06.002
OpenAlex ID: W1982728886
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DOI: 10.1016/J.JCTA.2006.06.002
description: scientific article; zbMATH DE number 5129735