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A Hamming code can correct all combinations of π‘˜ or fewer errors if and only if the minimum distance between any two code words is at least:

(a) π‘˜ + 1

(b) π‘˜ βˆ’ 1

(c) 2π‘˜ + 1

(d) 2π‘˜ βˆ’ 1
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Answer: Option C) $2k+1$

To guarantee correction of up to $t$ errors in any case, the minimum Hamming distance in a block code must be $d_{min} = 2t + 1$

To guarantee error detection up to $t$ errors, the minimum distance between the valid codes must be $t+1$ , so that the received codeword does not match a valid codeword.

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