a$)$ Consider a $(255,223)$ Reed$-$Solomon code. Find its symbol size $($m$)$ and error correcting capability $(t)$ for this code.

b$)$ For a $(10,7)$ Reed$-$Solomon code over GF$(11),$ find the generator polynomial.

c$)$ For $($b$),$ develop symbol mapping table.

d$)$ For $($b$),$ calculate syndrome for $r(x)=x^5.$

e$)$Construct a recursive systematic convolutional encoder using the non$-$systematic convolutional encoder

f$)$ Find the state diagram of recursive systematic convolutional encoder developed in $($ e$).$

g$)$ Construct turbo encoder by $($i$)$ serial, $($ii$)$ parallel, and $($iii$)$ hybrid concatenation.

h$)$ By using odd$-$even interleaver for the turbo codes of previous part, encode message $10110001.$