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 $r(x)=x^5.$