The triple-error-correcting BCH(15, 5) code is constructed on the extended field GF(24). The extended field GF(24) is obtained using the primitive polynomial p (x) = x4 + x3 + 1. The data-word polynomial is
d(x) . x6 + x3 + x + 1. Assume that a data-word is encoded and the generated code-word c(x) is transmitted. The received word at the receiver side is expressed in polynomial form as
r(x) = c(x) + e(x) where e(x) = x4 + x2. Using r(x), determine the transmitted code-word using the PGZ algorithm.