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Biometrika 2005 92(2):385-397; doi:10.1093/biomet/92.2.385
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© 2005 Biometrika Trust

Some nonregular designs from the Nordstrom–Robinson code and their statistical properties

Hongquan Xu

Department of Statistics, University of California, Los Angeles, California 90095-1554, U.S.A. hqxu{at}stat.ucla.edu

The Nordstrom–Robinson code is a well-known nonlinear code in coding theory. This paper explores the statistical properties of this nonlinear code. Many nonregular designs with 32, 64, 128 and 256 runs and 7–16 factors are derived from it. It is shown that these nonregular designs are better than regular designs of the same size in terms of resolution, aberration and projectivity. Furthermore, many of these nonregular designs are shown to have generalised minimum aberration among all possible designs. Seven orthogonal arrays are shown to have unique word-length pattern and four of them are shown to be unique up to isomorphism.

Key Words: Generalised minimum aberration; Generalised resolution; Generalised word-length pattern; Linear programming; MacWilliams identity; Orthogonal array; Projectivity

Received June 2003. Revised July 2004.


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