Consider the code $BCH(15,7)$ whose generating polynomial $isg(X)=1+X^4+X^6+X^7+X^8.$

minimum distance $is5$ and ability $to$ correct $upto2$ errors $in$ the block.

Encode the message $m=[m_0,m_1,m_2,m_3,m_4,m_5,m_6]$ where each message bit $is$ given $by{m}_k=y_k$ mod $2,$ where

$x$ mod $2=\{\begin{array}{ccc}0,& x& \text{e}\text{v}\text{e}\text{n}\\ 1,& x& \text{o}\text{d}\text{d}\end{array}$

and $y_k=1823426$

The coded block must $bein$ systematic form, $c=[c_0,c_1,c_2,...c_{14}]=[b_0,b_1,b_2,...b_7,m_0,m_1...m_6],$ where $b=[b_0,b_{1,},...b_7]$ are the parity bits obtained from the message.