On Bounded Weight Codes
Information Theory
2010-09-21 v1 math.IT
Abstract
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.
Cite
@article{arxiv.1009.3657,
title = {On Bounded Weight Codes},
author = {Christine Bachoc and Venkat Chandar and Gerard Cohen and Patrick Sole and Aslan Tchamkerten},
journal= {arXiv preprint arXiv:1009.3657},
year = {2010}
}