MinT - Bound for Almost-MDS-Codes

Bound for Almost-MDS-Codes

[1, Theorem 4] states that a linear orthogonal array OA(b^m, s,F_b, m−1) / a linear [s, s−m, m]-code over F_b with

s = b(b – m + 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 F_b does not exist. This condition is satisfied if

4 ≤ m ≤ b for b odd and 5 ≤ m ≤ b−1 for b even, and
the MDS-code-conjecture holds in PG(m−2, b).

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: 2015-09-03. http://mint.sbg.ac.at/desc_CBoundT1Lin.html

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