Calculate the syndrome for the block coded and check that this block actually belongs $to$ the $BCH(15,7)$ code.

block coded $=[110011001001000]$

Considering the code $BCH(15,7)$ whose generating polynomial $isg(x)=1+x^4+x^6+x^7+x^8$and minimum distance $is$ equal $to5$ and the ability $to$ correct $upto2$ errors $in$ the block.