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, s1s2 – m1m2, k + 1]-code over Fb can be constructed based on a linear [s1, s1 – m1, k + 1]-code over Fbm2 and a linear [s2, s2 – m2, k + 1]-code over Fb.
Construction
Let φ : SM2↔A2 ⊆ Sbs2 denote an arbitrary bijection. If A1 and A2 are linear, let φ : Fbm2↔A2 be Fb-linear. Then the resulting OA is defined as
See Also
Generalization for arbitrary OOAs
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: 2015-09-03.
http://mint.sbg.ac.at/desc_CConcatK.html