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December 2012 A code arithmetic approach for quaternary code designs and its application to (1/64)th-fractions
Frederick K. H. Phoa
Ann. Statist. 40(6): 3161-3175 (December 2012). DOI: 10.1214/12-AOS1069


The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The present paper aims at exploring the fundamental structure and developing a theory to characterize the wordlengths and aliasing indexes for a general $(1/4)^{p}$th-fraction QC design. Then the theory is applied to $(1/64)$th-fraction QC designs. Examples are given, indicating that there exist some QC designs that have better design properties, and are thus more cost-efficient, than the regular fractional factorial designs of the same size. In addition, a result about the periodic structure of $(1/64)$th-fraction QC designs regarding resolution is stated.


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Frederick K. H. Phoa. "A code arithmetic approach for quaternary code designs and its application to (1/64)th-fractions." Ann. Statist. 40 (6) 3161 - 3175, December 2012.


Published: December 2012
First available in Project Euclid: 22 February 2013

zbMATH: 1296.62154
MathSciNet: MR3097973
Digital Object Identifier: 10.1214/12-AOS1069

Primary: 62K15

Keywords: Aliasing index , generalized minimum aberration , generalized resolution , generalized wordlength pattern , Quaternary-code design , structure periodicity

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 6 • December 2012
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