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

C = {(xi,yi)  :  i = 1,…, N}.

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

($\displaystyle \begin{array}{cc} \vec{G}_{1} & \vec{G}_{2})\end{array}$.

See Also

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: 2008-04-04. http://mint.sbg.ac.at/desc_OJuxtaposition.html

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