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 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.