Discussion

What is the minimum Hamming distance for detection of six errors or correction of two errors ?

Answer: A

The minimum Hamming distance is 7.

To detect s errors a code needs \(d_{min} = s + 1\); to correct t errors it needs \(d_{min} = 2t + 1\).

\[ \begin{aligned} \text{detect 6:}\ d_{min} &= 6 + 1 = 7 \\ \text{correct 2:}\ d_{min} &= 2(2) + 1 = 5 \end{aligned} \]

A distance of 7 meets both requirements, while 5 allows correcting two errors but detects only up to four. 3 and 1 are too small for either.

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