Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On codes in the projective linear group $PGL(2,q)$   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.

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The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org