Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ranks of propelinear perfect binary codes   It is proven that for any numbers n=2^m-1, m >= 4 and r, such that n -
log(n+1)<= r <= n excluding n = r = 63, n = 127, r in {126,127} and n = r =
2047 there exists a propelinear perfect binary code of length n and rank r.

24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat