Construction XX with a Chain of Cyclic Codes

Given three linear [s, ni, di]-codes C1C2C3 and two additional codes C4, C5 with parameters [s4, n3n1, d4] and [s5, n3n2, d5], all over the same field, a new [s + s4 + s5, n3, d]-code with

d = min{d1, d2 + d4, d3 + d4 + d5}

can be constructed.

This construction is a special case of construction XX, which requires only C1C3 instead of C1C2.

Special Cases

Applications

MinT applies this method in all situations where construction X is applied and chains containing at least 3 subcodes are available.

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 XX with a Chain of Cyclic Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CConsXX3-Cyclic.html

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