## Concatenation of Two Orthogonal Arrays

Given two (linear) orthogonal arrays A_{1}, A_{2} with parameters OA(*M*_{1}, *s*_{1}, *S*_{M2}, *k*) and OA(*M*_{2}, *s*_{2}, *S*_{b}, *k*), a new (linear) OA(*M*_{1}, *s*_{1}*s*_{2}, *S*_{b}, *k*) can be constructed. Using duality, a linear [*s*_{1}*s*_{2}, *s*_{1}*s*_{2} – *m*_{1}*m*_{2}, *k* + 1]-code over **F**_{b} can be constructed based on a linear [*s*_{1}, *s*_{1} – *m*_{1}, *k* + 1]-code over **F**_{bm2} and a linear [*s*_{2}, *s*_{2} – *m*_{2}, *k* + 1]-code over **F**_{b}.

### Construction

Let *φ* : *S*_{M2}↔A_{2} ⊆ *S*_{b}^{s2} denote an arbitrary bijection. If A_{1} and A_{2} are linear, let *φ* : **F**_{bm2}↔A_{2} be **F**_{b}-linear. Then the resulting OA is defined as

*φ*(

*x*

_{i}))

_{i=1,…, s1}:

*∈ A*

**x**_{1}}.

### See Also

Generalization for arbitrary OOAs

### Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.

Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Concatenation of Two Orthogonal Arrays.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2008-04-04.
http://mint.sbg.ac.at/desc_CConcatK.html