A $(7,5)$ Reed$-$Solomon code used for erasure decoding is defined by the generator polynomial g$($x$)=($x $+\backslash$alpha $)($x $+\backslash$alpha

$2$

$)$ in GF$(23$

$).$ The GF$(23$

$)$ is specified by Table $2.$

Table $2$: Construction of a GF$(23$

$)$ field by h$($x$)=1+$ x $+$ x

$3$