Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proofs of Two Conjectures On the Dimensions of Binary Codes   Let $\mathcal{L}$ and $\mathcal{L}_0$ be the binary codes generated by the
column $\mathbb{F}_2$-null space of the incidence matrix of external points
versus passant lines and internal points versus secant lines with respect to a
conic in $PG(2, q)$, respectively. We confirm the conjectures on the dimensions
of $\mathcal{L}$ and $\mathcal{L}_0$ using methods from both finite geometry
and modular representation theory.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci