1. The generator polynomial of the double-error-correcting BCH(15, 7) cyclic code is given as
g (x) = x8 + x7 + x6 + x4 + 1:
The data-word polynomial is d(x) = x6 + x3 + x + 1. Obtain the systematic and non-systematic code-words for d(x).
2. For any triple-error-correcting BCH code, find the coefficients of error location polynomial in terms the syndromes.