On codes in the projective linear group $PGL(2,q)$
Tao Feng, Weicong Li, Jingkun Zhou · arXiv (Cornell University) · 2020
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 $A=\{g\in G: g^{q+1}= 1,\, g^2 e 1 \}$, then $λG=A\cdot D$, where $λ=q$ or $q-1$ according as $q$ is even or odd.