Restricted Johnson Bound

Let Ab(s, d, w) denote the maximum number of code words of a constant-weight (s, N, d)-code.

MinT uses the following methods for obtaining an upper bound on Ab(s, d, w):

Trivial Cases

Special Results

Upper Bounds

In those cases where the exact value of Ab(s, d, w) is not known, MinT uses the strongest of the following bounds. Note that the first two of these bounds are recursive.

References

[1]F. Jessie MacWilliams and Neil J. A. Sloane.
The Theory of Error-Correcting Codes.
North-Holland, Amsterdam, 1977.
[2]Selmer M. Johnson.
A new upper bound for error-correcting codes.
IEEE Transactions on Information Theory, 8(3):203–207, April 1962.
[3]Selmer M. Johnson.
On upper bounds for unrestricted binary error-correcting codes.
IEEE Transactions on Information Theory, 17(4):466–478, July 1971.
[4]Andries E. Brouwer.
Bounds on the size of linear codes.
In Vera S. Pless and W. Cary Huffman, editors, Handbook of Coding Theory, volume 1, pages 295–461. Elsevier Science, 1998.

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. “Restricted Johnson Bound.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_CBoundRestrictedJohnson.html