Concatenation of Two Orthogonal Arrays

Given two (linear) orthogonal arrays A1, A2 with parameters OA(M1, s1, SM2, k) and OA(M2, s2, Sb, k), a new (linear) OA(M1, s1s2, Sb, k) can be constructed. Using duality, a linear [s1s2, s1s2m1m2, k + 1]-code over Fb can be constructed based on a linear [s1, s1m1, k + 1]-code over Fbm2 and a linear [s2, s2m2, k + 1]-code over Fb.

Construction

Let φ : SM2A2Sbs2 denote an arbitrary bijection. If A1 and A2 are linear, let φ : Fbm2A2 be Fb-linear. Then the resulting OA is defined as

{(φ(xi))i=1,…, s1  :  xA1}.

See Also

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. “Concatenation of Two Orthogonal Arrays.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CConcatK.html

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