Prove that a random q-ary code with rate R > 0 with high probability has relative distance 8 2 H,' (1 – 2R –- €). Note that this is worse than the bound for random linear codes in Hint : Your argument should show that the probability of having distance at least dZH-1q(1-2R-E)d2Hq-1(1-2R-e) is 1-0(1)1-0(1), i.e. the probability should go to 1 as the block length n→o
Prove that a random q-ary code with rate R > 0 with high probability has relative distance 8 2 H,' (1 – 2R –- €). Note that this is worse than the bound for random linear codes in Hint : Your argument should show that the probability of having distance at least dZH-1q(1-2R-E)d2Hq-1(1-2R-e) is 1-0(1)1-0(1), i.e. the probability should go to 1 as the block length n→o
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Prove that a random q-ary code with rate R> 0 with high probability has relative distance
8 > H7'(1 – 2R – E). Note that this is worse than the bound for random linear codes in
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Hint : Your argument should show that the probability of having distance at least
dzH-1q(1-2R-e)ōzHq-1(1-2R-e) is 1-0(1)1-0(1), i.e. the probability should go to 1 as the block
length n→o
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