GATE 2025 EC – Question 33
The generator matrix of a (6,3) binary linear block code is given by
$$G=\begin{bmatrix}1&0&0&1&0&1\\0&1&0&0&1&1\\0&0&1&1&1&0\end{bmatrix}.$$
The minimum Hamming distance $d_{min}$ between codewords equals ________ (answer in integer).
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Show answer and explanation
Correct answer: 3
Explanation
For a linear code $d_{min}$ is the minimum weight of a non-zero codeword. The rows have weights 3, 3, 3. The sums of two rows are 110110, 101011, 011101 (weight 4 each). The sum of all three rows is 111000 (weight 3). So the minimum non-zero weight is 3.