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{1069362743,
author = {Suen, Chung-Yi and Chen, Hegang and Wu, C. F. J.},
title = {Some identities on $q\sp {n-m}$ designs with application to minimum aberration designs},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 1176-1188},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362743}
}
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., Tome 25 (1997) no. 6, pp. 1176-1188. http://gdmltest.u-ga.fr/item/1069362743/