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, s−m, m]-code over Fb with m > b is always a near-MDS code [1].
Thus, if an [s, s−m, m]-code over Fb with m > b exists, its dual is an [s, m, s−m]-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.”
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Version: 2024-09-05.
http://mint.sbg.ac.at/desc_CDualT1IsT1.html