Let C be the nullspace of the 1 x 9 matrix H1 (6.2.6) In other words, let C be the parity check code of length 9 (8 data bits, 1 parity check bit) (a) Use our standard methods to find a basis B for C. (b) What is the dimension of C? In general, what will the dimension of the parity check code of length n be? (c) Let G be the matrix whose columns are the vectors in the basis B from part (a). For a given message bitstring m, explain why the encoding procedure of Example 6.2.8 is equivalent to transmitting x-Gm.
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