Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binary extremal self-dual codes of length $60$ and related codes   We give a classification of four-circulant singly even self-dual $[60,30,d]$
codes for $d=10$ and $12$. These codes are used to construct extremal singly
even self-dual $[60,30,12]$ codes with weight enumerator for which no extremal
singly even self-dual code was previously known to exist. From extremal singly
even self-dual $[60,30,12]$ codes, we also construct extremal singly even
self-dual $[58,29,10]$ codes with weight enumerator for which no extremal
singly even self-dual code was previously known to exist. Finally, we give some
restriction on the possible weight enumerators of certain singly even self-dual
codes with shadow of minimum weight $1$.

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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom