$4.$ A systematic $(7,4)$ Hamming code has generator matrix $100001$ $01$ $011$ $00101$ $1000111$ $($a$)$ What are $,$ $,$ $,$ & $?($b$)$ Suppose the demodulated data word is rn $=0,1,0,1,1,0$; $1.$ What is the syndrome? $($c$)$ Given the syndrome from $($b$),$ what is the decoded message word $($i$.$e$.,$ mn$)?$