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arXiv · 1207.1934

Generalized wordlength patterns and strength

Jay H. Beder·Jesse S. Beder
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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.

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Jay H. Beder, Jesse S. Beder. 2012-07-09. Generalized wordlength patterns and strength. https://doi.org/10.1016/j.jspi.2012.06.015

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