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Limit distribution of the minimum distance of random linear codes

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1 Author(s)

The distribution of the ratio of minimum distance to code length of a random linear code approaches a step distribution as the code length becomes arbitrarily large at fixed code rate. The location of the step is at the smaller value of p satisfying 1 + p \log _{2}p + (1 - p) \log _{2} (1 - p) = k/n .

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IEEE Transactions on Information Theory  (Volume:13 ,  Issue: 4 )