Use cycling redundancy code $($CRC$)$ error detection method to answer the following parts

$($i$)$ Find the cycling redundancy code $($CRC$)$ for $1110010101$ with the divisor x$3+$ x$2+1$

$($ii$)$ Suppose that we want to transmit the message $11001001$ and protect it from error using the CRC polynomial x$3+1.$ Use the division method in CRC encoder, determine the message that should be transmitted?

$($iii$)$ Corrupt the left$-$most third bit of the transmitted message $($obtained in the previous part$)$ and show that the error is detected by the receiver using CRC technique.