Repeating Each Code Word

Every (linear) (s, N, d)-code yields a (linear) (us, N, ud)-code over the same field for all u ≥ 1. Therefore every linear orthogonal array OA(bm, s, Sb, k) yields a linear OA(bm+(u−1)s, us, Sb, u(k + 1) − 1).

Construction for Linear Codes

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

This construction is equivalent to concatenation with a [u, 1, u]-repetition code over Fb. It is also equivalent to a (u−1)-times juxtaposition of the code with itself.

Construction for Linear Orthogonal Arrays

For linear orthogonal arrays this construction is most easily performed using the dual 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.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04.

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