Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the third weight of generalized Reed-Muller codes   In this paper, we study the third weight of generalized Reed-Muller codes. We
prove under some restrictive condition that the third weight of generalized
Reed-Muller codes depends on the third weight of generalized Reed-Muller codes
of small order with two variables. In some cases, we are able to determine the
third weight and the third weight codewords of generalized Reed-Muller codes.

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc