Construction X with Varšamov–Edel Bound

Construction X allows the construction of a new code based on three linear codes C1, C2, and Ce, where C1 is a subcode of C2, and Ce is an appropriately chosen auxiliary code.

Obtaining Code and Subcode Using the Varšamov-Edel Bound

Let C1ʹ denote a linear [s1, n1, d1]-code. Choose a d2 < d1 and apply Varšamov-Edel lengthening to C1ʹ, which is also an [s1, n1, d2]-code. The result is an [s2, n2, d2]-code C2, which contains as a subcode the [s2, n1, d1]-code C1 obtained from C1ʹ by embedding in the larger space Fbs2. Now construction X can be applied to C1C2.

Since C2 is not available explicitly, this method is considered non-constructive.

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. “Construction X with Varšamov–Edel Bound.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CConsXVarshamovEdel.html

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