## OOA Duplication

Every (linear) ordered orthogonal array OOA(*b*^{m}, *s*, *S*_{b}, *T *, *k*) yields a (linear) OOA(*b*^{m+1}, *s*, *S*_{b}, *T *, *k*). Correspondingly, every linear [(*s*, *T *), *n*, *d*]-NRT-code with *n* > 0 yields a linear [(*s*, *T *), *n*−1, *d*]-code over the same field.

Applying this propagation rule *T * times is equivalent to embedding in a larger space once and discarding factors / shortening *T * times. However, the result of less than *T * applications cannot be achieved by any other combination of propagation rules.

### Construction for OOAs

The new OOA Aʹ is obtained by replicating each run of the original OOA Aʹ *b* times or by appending an arbitrary row to the generator matrix of A. If A is simple, linear, and *m* < *sT *, a new OOA without duplicate runs can be obtained by appending one row to the generator matrix such that the resulting matrix has full rank.

### Construction for Linear NRT-Codes

The new code Cʹ is obtained by taking an arbitrary subspace of dimension *n*−1 of C or by dropping one row from the generator matrix of C.

### See Also

Special case for OAs / linear codes

For

*T*→∞ one obtains the corresponds result for nets

### 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. “OOA Duplication.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2008-04-04.
http://mint.sbg.ac.at/desc_ODuplication.html