The Annals of Statistics

Some identities on $q\sp {n-m}$ designs with application to minimum aberration designs

Hegang Chen, C. F. J. Wu, and Chung-Yi Suen

Full-text: Open access


Chen and Hedayat and Tang and Wu studied and characterized minimum aberration $2^{n-m}$ designs in terms of their complemetary 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.

Article information

Ann. Statist., Volume 25, Number 3 (1997), 1176-1188.

First available in Project Euclid: 20 November 2003

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K15: Factorial designs
Secondary: 62K05: Optimal designs

Fractional factorial design linear code MacWilliams identities resolution projective geometry weight distribution wordlength pattern


Suen, Chung-Yi; Chen, Hegang; Wu, C. F. J. Some identities on $q\sp {n-m}$ designs with application to minimum aberration designs. Ann. Statist. 25 (1997), no. 3, 1176--1188. doi:10.1214/aos/1069362743.

Export citation