Show that we can correctly decode the Repetitionℓ code as follows: given a bitstring c ′ , for each bit position i, we take the majority vote of the ℓ blocks’ ith bit in c ′ , breaking ties...

Show that we can correctly decode the Repetitionℓ code as follows: given a bitstring c ′ , for each bit position i, we take the majority vote of the ℓ blocks’ ith bit in c ′ , breaking ties arbitrarily. (In other words, prove that this algorithm actually gives the codeword that’s closest to c ′ .)

In some error-correcting codes, for certain errors, we may be able to correct more errors than Theorem 4.1 suggests: that is, the minimum distance is 2t + 1, but we can correct certain sequences of > t errors. We’ve already seen that we can’t successfully correct every such sequence of errors, but we can successfully handle some sequences of errors using the standard algorithm for error correction (returning the closest codeword)