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(bm, s, Sb, T , k) yields a linear OA(bm+(u−1)sT, us, Sb, 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


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: 2008-04-04.

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