Limit distribution of the minimum distance of random linear codes

  • Authors:

  • J. Pierce

  • Affiliations:

  • -

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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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.