In BCH generator matrix is calculated by taking lcm of minimal polynomials. For example generator polynomial for GF(32) is following
$ m1(x) = x^5 + x^2 + 1$
$ m3(x) = x^5 + x^4 + x^3 + x^2 + 1$
$m5(x) = x^5 + x^4 + x^2 + x + 1$
$g(x) = x^{15} + x^{11} + x^{10} + x^9 + x^8 + x^7 + x^5 + x^3 + x^2 + x + 1 $
My question is how can i write generator polynomial to generator matrix?
How can i calculate parity check matrix for BCH?