Show that the Hamming distance is a metric on V" the set of all words of
Compare the Hamming metric and the Levenshtein metric on the set V". Is
either metric, in general, always less than or equal to the other? Prove your
We say that a code of length p corrects n errors if every word in VP is within
distance n of a unique codeword in the code.
(a) In VS. find an example of a code C that has four codewords and corrects
(b) Show that four codewords is the maximal size for a code in V8 that corrects
For each of the following, find the Levenshtein distance between the two se-
quences, x andy. In cases where the sequences have equal length, also compute
the Hamming distance.
(a) x = ACGGTAT and y = GGTAG
(b) x = CTGGTAC and y = CTAGATC
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