Bound for Almost-MDS-Codes
[1, Theorem 4] states that a linear orthogonal array OA(bm, s,Fb, m−1) / a linear [s, s−m, m]-code over Fb with
s = b(b – m + 4) + 1 + 
cannot exist, provided that the [b + 2,(b + 2) - (m−1), m]-MDS code over Fb 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.”
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Version: 2024-09-05.
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