Considering the code $BCH(15,7)$ whose generating polynomial $isg(x)=1+x^4+x^6+x^7+x^8$ and minimum distance $is5$ and the ability $to$ correct $upto2$ erros.

Suppose that the system's communication channel presents a bit error rate given $p=4*{10}^{-4}$

Calculate the bit error rate that will $be$ obtained after decoding $if$ the transmission system employ the $BCH(15,7)$ code for channel coding.