Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotically optimal Boolean functions   The largest Hamming distance between a Boolean function in $n$ variables and
the set of all affine Boolean functions in $n$ variables is known as the
covering radius $\rho_n$ of the $[2^n,n+1]$ Reed-Muller code. This number
determines how well Boolean functions can be approximated by linear Boolean
functions. We prove that \[ \lim_{n\to\infty}2^{n/2}-\rho_n/2^{n/2-1}=1, \]
which resolves a conjecture due to Patterson and Wiedemann from 1983.

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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex