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I found this problem in here
(Problem 6 on page 6)

Consider the triple repeat code. What codewords are closest to $(1, 1, 0)$? Describe the set of vectors at distance $1$ or less from the codeword $(0, 0, 0)$. Do the same for the set of vectors at distance $1$ or less from the codeword $(1, 1, 1)$. What is the relation between these two sets? (We think of them as balls of radius one around the respective codewords.) What is the distance between the codewords $(0,0, 0)$ and $(1, 1, 1)$?

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    by "distance" do you mean the $\operatorname{norm}$ in the particular vector space2012-04-23
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    What have you tried? @Bidit, I'm fairly sure that the Hamming metric is the relevant distance here.2012-04-23
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    It's on page 5: Hamming distance between two vectors: H(v; w) = number of positions in which v and w differ (19)2012-04-23
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    @JyrkiLahtonen oh, I missed that. Thanks2012-04-23
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    Megan, this is a small problem. As this is probably your first exercise in coding theory, you could simply list all the 8 binary vectors of length 3, and calculate their Hamming distances from the two codewords. Trust me, it won't take you too long, and gives you a feeling of how the Hamming distance works.2012-04-23

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