On Bounded Weight Codes
The maximum size of a binary code is studied as a function of its length, minimum distance d, and minimum code-word weight. This function B(n, d, w) is first characterized in terms of its exponential growth rate in the limit n -> infinity for fixed delta = d/n and omega = 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 0 <= omega <= 1/2, and equal to the exponential growth rate of A (n, d, w) for 1/2 < omega <= 1. Second, analytic and numerical upper bounds on B (n, d, w) are derived using the semidefinite programming (SDP) method. These bounds yield a nonasymptotic improvement of the second Johnson bound and are tight for certain values of the parameters.
semidefinite programming johnson bounds constant weight codes