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Limit distribution of the minimum distance of random linear codes

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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 ofpsatisfying1 + p log_{2}p + (1 - p) log_{2} (1 - p) = k/n.

Published in:

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

Date of Publication:

October 1967

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