Limit distribution of the minimum distance of random linear codes
- 1 October 1967
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 13 (4) , 595-599
- https://doi.org/10.1109/TIT.1967.1054053
Abstract
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.Keywords
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