Arbitrary OOA / Dual of Arbitrary NRT-Code (with Infinite s)
A linear ordered orthogonal array OOA(bm, s, Sb, T , k) with strength k = 0 exists for all m and all s ≥ m/T . Its dual is a linear [(s, T ), sT −m, 1]-NRT-code over Fq.
The OOA (Arbitrary OOA)
Every OOA(bm, s, Sb, T , k) has strength k = 0. It can be generated by any m×(s, T )-matrix over Fb with full rank (e.g. by the first m rows of the (s, T )×(s, T )-identity matrix).
Its Dual Code (Arbitrary NRT-Code)
Every non-singular n×(s, T )-matrix over Fb defines an [(s, T ), n, 1]-code over Fb.
See Also
Special case for OAs / linear codes
For T →∞ the corresponding result for nets is obtained
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. “Arbitrary OOA / Dual of Arbitrary NRT-Code (with Infinite s).”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2024-09-05.
http://mint.sbg.ac.at/desc_OK0-inf.html