(a) (i) Write down a parity-check matrix for the code Ham(2, 7). (ii) Using your parity-check matrix, explain why the minimum distance of Ham(2, 7) is exactly 3. (b) Consider the linear code C over F, with the following parity-check matrix: (3 1 1 0 2 30 1 (i) Decide whether or not C is an MDS code. Justify your answer. (ii) Suppose that the above matrix is instead taken to be the generator matrix of a linear code D over F7. Is D an MDS code? Justify your answer.

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