Signed Differences for Weighing Designs

In this paper, an alternative, support based, definition of periodic and nonperiodic autocorrelation function is presented. The approach is shown to require significantly less computational effort and is suitable for the construction of large weighing designs, even by hand. The proposed definitions...

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Bibliographic Details
Published in:Sankhyā. Series B (2008) 2010-05, Vol.72 (1), p.107-121
Main Author: Georgiou, Stelios D.
Format: Article
Language:English
Subjects:
Autocorrelation
Correlation analysis
Design
Integers
Life tables
Linear models
Mathematical sequences
Mathematical tables
Mathematics and Statistics
Matrices
Matrix
Numbers
Statistics
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Summary:In this paper, an alternative, support based, definition of periodic and nonperiodic autocorrelation function is presented. The approach is shown to require significantly less computational effort and is suitable for the construction of large weighing designs, even by hand. The proposed definitions are applied then to find weighing designs W(2n; 9) constructed by two circulant matrices. All possible ways the weight 9 can be split into two weights is also investigated. Solutions for each split, if they exist, are classified for weighing matrices W(2n; 9); for all n up to 250. Partial results are also presented for weighing matrices W(2n; 9) for n up to 400.
ISSN:0976-8386
0976-8394
DOI:10.1007/s13571-010-0007-3