Generalized wordlength patterns and strength

Abstract

Xu and Wu (2001) defined the \emph{generalized wordlength pattern} $(A_1,...,A_k)$ of an arbitrary fractional factorial design (or orthogonal array) on $k$ factors. They gave a coding-theoretic proof of the property that the design has strength $t$ if and only if $A_1=...=A_t=0$. The quantities $A_i$ are defined in terms of characters of cyclic groups, and so one might seek a direct character-theoretic proof of this result. We give such a proof, in which the specific group structure (such as cyclicity) plays essentially no role. Nonabelian groups can be used if the counting function of the design satisfies one assumption, as illustrated by a couple of examples.

References in corpus (1)

• Geometric isomorphism and minimum aberration for factorial designs with quantitative factors