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Consider the (7, 4) Hamming code defined by the generator

Consider the (7, 4) Hamming code defined by the generator

Consider the (7, 4) Hamming code defined by the generator polynomial g(X) = 1 + X + X3 the code word 0111001 is sent over a noisy channel, producing the received word 0101001 that has a single error. Determine the syndrome polynomial s(X) for this received word, and show that it is identical to the error polynomial e(X).

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