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Statistica Sinica 17(2007), 1191-1213



Hongquan Xu and Alan Wong

University of California, Los Angeles

Abstract: A quaternary linear code is a linear space over the ring of integers modulo 4. Recent research in coding theory shows that many famous nonlinear codes such as the Nordstrom and Robinson (1967) code and its generalizations can be simply constructed from quaternary linear codes. This paper explores the use of quaternary codes to construct two-level nonregular designs. A general construction of nonregular designs is described, and some theoretic results are obtained. Many nonregular designs constructed by this method have better statistical properties than regular designs of the same size in terms of resolution and aberration. A systematic construction procedure is proposed and a collection of nonregular designs with 16, 32, 64, 128, 256 runs and up to 64 factors is presented.

Key words and phrases: Fractional factorial design, generalized minimum aberration, generalized resolution, MacWilliams identity, quaternary code.

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