OOA Duplication
Every (linear) ordered orthogonal array OOA(bm, s, Sb, T , k) yields a (linear) OOA(bm+1, s, Sb, 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: 2024-09-05.
http://mint.sbg.ac.at/desc_ODuplication.html