Sharpened Johnson Bound

In [1] a sharpened version of the Johnson bound is presented, which establishes the non-existence of linear [2^u – 2, 2^u − 2u−1, 5]-codes over ℤ₂ for u ≥ 4.

This result rules out linear codes with the parameters of Kerdock and Preparata codes.

References

[1]	Andries E. Brouwer and L. M. G. M. Tolhuizen. A sharpening of the Johnson bound for binary linear codes and the nonexistence of linear codes with Preparata parameters. Designs, Codes and Cryptography, 3(2):95–98, May 1993. doi:10.1007/BF01388407 MR1218941 (94d:94009)

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. “Sharpened Johnson Bound.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_CBoundSharpenedJohnson.html