Some identities on \(q^{n-m}\) designs with application to minimum aberration designs. (English) Zbl 0898.62095

Suen, Chung-yi; Chen, Hegang; Wu, C. F. J.

Ann. Stat. 25, No. 3, 1176-1188 (1997).

Summary: H. Chen and A. S. Hedayat [ibid. 24, No. 6, 2536-2548 (1996; Zbl 0867.62066)] and B. Tang and C. F. J. Wu [ibid. 2549-2559 (1996; Zbl 0867.62068)] studied and characterized minimum aberration \(2^{n-m}\) design in terms of their complementary designs. Based on a new and more powerful approach, we extend the study to identify minimum aberration \(q^{n-m}\) designs through their complementary designs. By using MacWilliams identities and Krawtchouk polynomials in coding theory, we obtain some general and explicit relationships between the wordlength pattern of a \(q^{n-m}\) design and that of its complementary design. These identities provide a powerful tool for characterizing minimum aberration \(q^{n-m}\) designs. The case of \(q=3\) is studied in more details.

MSC:

62K15

Factorial statistical designs

Keywords:

fractional factorial design; linear code; resolution; projective geometry; weight distribution; MacWilliams identities; Krawtchouk polynomials; wordlength pattern

Citations:

Zbl 0867.62068; Zbl 0867.62066