This problem is related to single limited magnitude $l$ error, where $l$ can

be $+1$ or $-1.$ Assume the digits are over $Z_5.$

$($a$)$ If the number of information digits, $k,$ is $8$ then what is the mini$-$

mum number of check digits, $r,$ required to do the error correction?

$($b$)$ Find the parity check matrix $H$ in systematic form.

$($c$)$ If the given information word is $42221321,$ find the codeword.

$($d$)$ If the first digit of the information word is changed from $4$ to $3($i$.$e$.,$

$-1$ error$)$ show how error correction is done.