$(2)[35$ points$]$ Figure $1$ illustrates $\backslash ((3,1)\backslash )$ repetition code and $\backslash ((3,2)\backslash )$ parity code in $($a$)$ and $($b$),$ respectively.

:ods

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$($b$)$

Fig. $1$: Repitition code and Parity code

$($a$)$ Describe the general relation between Hamming distance $\backslash ($ d$\_\{\backslash$text $\{$min $\}\}\backslash )$ and the number of error bit, $\backslash ($ t $\backslash )$ for two cases: $($i$)$ Error Detectable Code; $($ii$)$ Error Correctable Code. $[10$ points$]$

$($b$)$ For two error bits that cause changing the original bits $(000)$ to $(110),$ describe the way to detect the error and the way to correct the error at the receiver for each of repetition and parity codes. If the receiver cannot detect and$/$or correct the error, clearly explain. $[25$ points$]$