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

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

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