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) . x 5 + x 3 + 1. 2. The extended field GF (24) is...

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.