Concatenation of Two Codes

Given a linear [s1, n1, d1]-code C1 over Fbn2 and a linear [s2, n2, d2]-code C2 over Fb, a linear [s1s2, n1n2, d1d2]-code over Fb can be constructed. Using duality, a linear orthogonal array OA(bs1s2-n1n2, s1s2,Fb, d1d2 − 1) can be constructed based on a linear OA(bs1-m1, s1,Fbs2-n2, d1 − 1) and OA(bs2-m2, s2,Fb, d2 − 1).

Construction

Let φ : Fbn2C2Fbs2 denote an arbitrary Fb-linear bijection. The new code C is given by

C = {(φ(xi))i=1,…, s1  :  xC1).

Special Cases

A number of other propagation rules can be interpreted as concatenation with special codes:

See Also

References

[1]Jürgen Bierbrauer.
Introduction to Coding Theory.
Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton, London, New York, Washington D.C., 2004.
MR2079734 (2005f:94001)

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 Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CConcatD.html

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