  In this paper, we resolve a conjecture of Green and Liebeck [Disc. Math., 343
(8):117119, 2019] on codes in $PGL(2,q)$. To be specific, we show that: if $D$
is a dihedral subgroup of order $2(q+1)$ in $G=PGL(2,q)$, and $A=\{g\in G:
g^{q+1}= 1,\, g^2\ne 1 \}$, then $\lambda G=A\cdot D$, where $\lambda=q$ or
$q-1$ according as $q$ is even or odd.
