BACHOC, Christine; CHANDAR, Venkat; COHEN, Gerard; SOLE, Patrick; TCHAMKERTEN, Aslan

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BACHOC, Christine
Institut de Mathématiques de Bordeaux [IMB]

CHANDAR, Venkat

COHEN, Gerard
Ministère de la Culture et de la communication, service du Livre et de la lecture, bureau du Patrimoine

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IEEE Transactions on Information Theory. 2011, vol. 57, n° 10, p. 6780-6787

Institute of Electrical and Electronics Engineers

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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.< Réduire

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On Bounded Weight Codes

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