$5\mathrm{.}4\mathrm{.}3$ fJ is a primitive element of GF$(24)$ constructed using the irreducible polynomial

p$($x$)=1+$x$3+$x$4.$ Find the generator polynomial g$($x$)$ the $2-$errorcorrecting

BCH code of length $15$ using this representation of GF$(24)$; that is$,$

find g $($x$)=$ m $1($x $)$m $3($x$).($See Exercise $5\mathrm{.}1\mathrm{.}15)$