1. Find the generator and parity check matrices of the double-error-correcting BCH code. Use GF(25) constructed using the primitive polynomial p(x) . x5 + x3 + 1.
2. The extended field GF(24) is constructed using the primitive polynomial p (x) . x4 + x + 1. The generator polynomial of the triple-error-correcting BCH (15, 5) code over GF(24) is evaluated as
G(x) = x10 + x8 + x5 + x4 + x2 + x + 1:
Find the parity check and generator matrices of the dual code.