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  1. Encode the data vector d = [α3 α2 α α4 α2] using the generator polynomial of the Reed-Solomon code RS(7, 5) designed in problem 1.
  2. Construct the generator polynomial of three-error-correcting Reed-Solomon code over GF(24) which is obtained using the primitive polynomial p(x) = x4 + x2 + 1.

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