Some new results on circulant weighing matrices
type: Item
instance of: scholarly article
title: Some new results on circulant weighing matrices
zbMATH Open document ID: 1007.05029
DOI: 10.1023/A:1011903510338
author: K. T. Arasu
author: Siu Lun Ma
published in: Journal of Algebraic Combinatorics
publication date: 2002-08-20T00:00:00Z
review text: A circulant weighing matrix \(C(n,k)\) is a circulant matrix \(C\) of size \(n\) with entries \(\{0,\pm 1\}\in \mathbb{Z}\) such that \(C\cdot C^T=k\cdot \mathbf{I}_n\) (\(\mathbf{I}_n\) identity matrix). It is interesting to obtain necessary and sufficient conditions on the existence of \(C(n,k)\)'s. Such conditions are known only for \(k=4\) and \(9\). The paper contains a nontrivial (though standard) application of algebraic number theory to obtain some necessary conditions in the cases \(k=25, 49\) and \(121\). Unfortunately, only finitely many examples can be ruled out.
reviewed by: Alexander Pott
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 1784339
zbMATH Keywords: weighing matrix
MaRDI profile type: Publication
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full work available at URL: a:1011903510338
OpenAlex ID: W2047975389
description: scientific article; zbMATH DE number 1784339