On codes in the projective linear group PGL(2,q)

Abstract

In this paper, we resolve a conjecture of Green and Liebeck (2019) [3] 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∈G:gq+1=1,g2≠1}, then λG=A⋅D, where λ=q or q−1 according as q is even or odd.