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arXiv · 1009.3657

On Bounded Weight Codes

Christine Bachoc·Venkat Chandar·Gerard Cohen·Patrick Sole·Aslan Tchamkerten
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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.

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Christine Bachoc, Venkat Chandar, Gerard Cohen, Patrick Sole, Aslan Tchamkerten. 2010-09-19. On Bounded Weight Codes. https://arxiv.org/abs/1009.3657

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