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On Bounded Weight Codes
The maximum size of a binary code is studied as a function of its length N,
minimum distance D, and minimum codeword weight W. This function B(N,D,W) is
first characterized in terms of its exponential growth rate in the limit as N
tends to infinity for fixed d=D/N and w=W/N. The exponential growth rate of
B(N,D,W) is shown to be equal to the exponential growth rate of A(N,D) for w <=
1/2, and equal to the exponential growth rate of A(N,D,W) for 1/2< w <= 1.
Second, analytic and numerical upper bounds on B(N,D,W) are derived using the
semidefinite programming (SDP) method. These bounds yield a non-asymptotic
improvement of the second Johnson bound and are tight for certain values of the
parameters
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