Question: Find the minimum distances of the codes given by these parity check matrices. (a) 1 0 0 1 0 0 0 001 10 1 1

Find the minimum distances of the codes given by these parity check matrices.

(a) 1 0 0 1 0 0 0 001 10 1 1

(a) 1 0 0 1 0 0 0 001 10 1 1 0 1 1 0 1 10 0 1 1 1 1 0 0 1 1 1 over Z2, 0 0 1 0 0 1 0 0 0 1 1 1 1 01 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 0 (b) (c) 1 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 over Z2, 0 0 10 1 10 1 0 0 0 1 1 1 1 0 2 106 1 0 0 0 1 3 0 4 3 2 over Z7, 4 0 4 6 0 35 (d) 1 1 0 0 0 10 01 1 1 1 000 over Z31. 0 1 0 1 0 1 1

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