Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On triply even binary codes   A triply even code is a binary linear code in which the weight of every
codeword is divisible by 8. We show how two doubly even codes of lengths m_1
and m_2 can be combined to make a triply even code of length m_1+m_2, and then
prove that every maximal triply even code of length 48 can be obtained by
combining two doubly even codes of length 24 in a certain way. Using this
result, we show that there are exactly 10 maximal triply even codes of length
48 up to equivalence.

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The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
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The categories of this paper are: cs
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin