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 ssi w. This function B(n, d, w) is first characterized in terms of its exponential growth rate in the limit n→∞ for fixed δ = d/n and ω = 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 ≤ ω ≤ 1/2, and equal to the exponential growth rate of A(n,d, w) for 1/2 <; ω ≤ 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.