Repeating Each Code Word for NRT-Codes

Every (linear) ((s, T ), N, d)-NRT-code yields a (linear) ((us, T ), N, ud)-code over the same field for all u ≥ 1. Therefore every linear ordered orthogonal array OOA(b^m, s, S_b, T , k) yields a linear OA(b^{m+(u−1)sT}, us, S_b, T , u(k + 1) − 1).

Construction for Linear NRT-Codes

The new code is constructed by repeating each code word u times.

This construction is equivalent to a (u−1)-times juxtaposition of the code with itself.

Construction for Linear OOAs

For linear OOAs this construction is most easily performed using the dual NRT-codes and the method described above.

See Also

• Special case for OAs / linear codes

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. “Repeating Each Code Word for NRT-Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_ORepeating.html