Juxtaposition for OOAs
Give an ((s1, T ), N, d1)-NRT-code, C1 and an ((s2, T ), N, d2)-code C2, an ((s1 + s2, T ), N, d1 + d2)-code over the same field can be constructed. Therefore a linear ordered orthogonal array OOA(b(s1+s2)T−n, s1 + s2, Sb, T , k1 + k2 + 1) can be constructed from a linear OOA(bs1T−n, s1, Sb, T , k1) and a linear OOA(bs2T−n, s2, Sb, T , k2).
Construction for Linear NRT-Codes
Let C1 = {x1,…,xN} and C2 = {y1,…yN}, then the new code C is given by
If the Ci are linear [(si, T ), n, di]-codes with generator matrices Gi, then C is an [(s1 + s2, T ), n, d1 + d2]-code with generator matrix
. See Also
Special case for OAs / linear codes
[1, Section 1.3, Problem (17)], [1, Figure 2.6], or [2, Section 10.2].
References
| [1] | F. Jessie MacWilliams and Neil J. A. Sloane. The Theory of Error-Correcting Codes. North-Holland, Amsterdam, 1977. |
| [2] | A. S. Hedayat, Neil J. A. Sloane, and John Stufken. Orthogonal Arrays. Springer Series in Statistics. Springer-Verlag, 1999. |
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. “Juxtaposition for OOAs.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2024-09-05.
http://mint.sbg.ac.at/desc_OJuxtaposition.html