Generalized (u, u+v)-Construction for OOAs

In [1, Theorem 4] the following generalization of the (u, u + v)-construction for OOAs is established, similar to the generalization of the (u, u + v)-construction for codes to generalized (u, u + v)-construction for codes.

Let C1,…, Cr be r ((si, T ), Ni, di)-NRT-codes, all over Fb, with b ≥ r and s1 ≤ ⋯ ≤ sr. Then an ((s, T ), N, d)-code over Fb with

s = $\displaystyle \sum_{{i=1}}^{{r}}$si,        N = $\displaystyle \prod_{{i=1}}^{{r}}$Ni,    and    d ≥ $\displaystyle \min_{{i=1,\ldots,r}}^{}$(r + 1 – i)di

can be constructed.

In the context of OOAs r linear OOAs A1,…, Ar with parameters OOA(bmi, si,Fb, T , ki) and s1 ≤ ⋯ ≤ sr can be used for constructing an OOA(bm1+…+mr, s1 + … + sr,Fb, T , k) with k = min{rk1 + (r – 1),(r – 1)k2 + (r – 2),…, 1kr +0}.

Special Cases

See Also

References

[1]Rudolf Schürer and Wolfgang Ch. Schmid.
MinT - new features and new results.
In Pierre LʹEcuyer and Art B. Owen, editors, Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 171–189. Springer-Verlag, 2009.
doi:10.1007/978-3-642-04107-5_10

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. “Generalized (u, u+v)-Construction for OOAs.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03. http://mint.sbg.ac.at/desc_OGeneralizedUUPlusV.html

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