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1. The extended field GF(23) is generated using the primitive polynomial p(x) = x3 + x2 + 1. Find the generator polynomial of the single-error-correcting Reed-Solomon code over GF(23).
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2. Express the data vector d . [α3 0 α4 α5 α2] in bit vector form. The elements of the data vector are chosen from GF(23) which is constructed using the primitive polynomial p(x) = x3 + x2 + 1.