Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The automorphism group of the doubly-even [72,36,16] code can only be of
  order 1, 3 or 5   We prove that a putative $[72,36,16]$ code is not the image of linear code
over $\ZZ_4$, $\FF_2 + u \FF_2$ or $\FF_2+v\FF_2$, thus proving that the
extremal doubly even $[72,36,16]$-binary code cannot have an automorphism group
containing a fixed point-free involution. Combining this with the previously
proved result by Bouyuklieva that such a code cannot have an automorphism group
containing an involution with fixed points, we conclude that the automorphism
group of the $[72,36,16]$-code cannot be of even order, leaving 3 and 5 as the
only possibilities.

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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg