Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Perfect Codes in the Johnson Graph   In this paper we consider the existence of nontrivial perfect codes in the
Johnson graph J(n,w). We present combinatorial and number theory techniques to
provide necessary conditions for existence of such codes and reduce the range
of parameters in which 1-perfect and 2-perfect codes may exist.

10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics