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On the fractional weight of distinct binary n -tuples (Corresp.)

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It is shown that the fractionpof ones in theMnpositions ofMdistinct binaryn-tuples satisfies the inequality begin{equation} h(p) geq (l/n) log_2 M end{equation} whereh(p) = - p log_2 p - (1 - p) log_2 (1 - p)is the binary entropy function. This inequality, which simplifies the derivation of the distance property of the Justesen codes, is proved using an elegant information-theoretic argument due to Kriz.

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Information Theory, IEEE Transactions on  (Volume:20 ,  Issue: 1 )