Bound for Almost-MDS-Codes

[1, Theorem 4] states that a linear orthogonal array OA(bm, s,Fb, m−1) / a linear [s, sm, m]-code over Fb with

s = b(bm + 4) + 1 + \begin{displaymath}\begin{cases}1 & (b-m+4)\mid b\\ 0 & \textrm{otherwise}\end{cases}\end{displaymath}

cannot exist, provided that the [b + 2,(b + 2) - (m−1), m]-MDS code over Fb does not exist. This condition is satisfied if

References

[1]Mario A. de Boer.
Almost MDS codes.
Designs, Codes and Cryptography, 9(2):143–155, October 1996.
doi:10.1007/BF00124590

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. “Bound for Almost-MDS-Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CBoundT1Lin.html

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