Question: The (5m, m) five-times repetition code has encoding function E: Zm2 Z5m2, where E(w) = wwwww. Decoding with D: Z5m2 Zm2 is accomplished

The (5m, m) five-times repetition code has encoding function E: Zm2 → Z5m2, where E(w) = wwwww. Decoding with D: Z5m2 → Zm2 is accomplished by the majority rule. (Here we are able to correct single and double errors made in transmission.)
(a) With p = 0.05, what is the probability for the transmission and correct decoding of the signal 0?
(b) Answer part (a) for the message 110 in place of the signal 0.
(c) For m = 2, decode the received word
r = 0111001001.
(d) If m = 2, find three received words r where D(r) = 00.
(e) For m = 2 and D: Z102 → Z22, what is | D-1(w) | for each w ∈ Z22?

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