Dual of a Near-MDS Code Is Again a Near-MDS Code

The dual code of a near-MDS code is again a near-MDS code. One has to be careful, because not every almost-MDS code (a code with Singleton defect t = 1) is also a near-MDS code. However, an [s, sm, m]-code over Fb with m > b is always a near-MDS code [1].

Thus, if an [s, sm, m]-code over Fb with m > b exists, its dual is an [s, m, sm]-code.

References

[1]Stefan M. Dodunekov and Ivan N. Landjev.
On near-MDS codes.
Journal of Geometry, 54(1–2):30–43, November 1995.
doi:10.1007/BF01222850

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. “Dual of a Near-MDS Code Is Again a Near-MDS Code.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CDualT1IsT1.html

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