1. The generator polynomial of the double-error-correcting Reed-Solomon code RS (7, 3) over GF(23), constructed using the primitive polynomial p(x) . x3 + x + 1, can be calculated as g(x) = x4 + α3 x3 + x2 + αx + α3:
The data-word polynomial is given as d(x) = α3 x2 + α2 x + α4. Systematically encode d(x).