Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The List-Decoding Size of Reed-Muller Codes   In this work we study the list-decoding size of Reed-Muller codes. Given a
received word and a distance parameter, we are interested in bounding the size
of the list of Reed-Muller codewords that are within that distance from the
received word. Previous bounds of Gopalan, Klivans and Zuckerman \cite{GKZ08}
on the list size of Reed-Muller codes apply only up to the minimum distance of
the code. In this work we provide asymptotic bounds for the list-decoding size
of Reed-Muller codes that apply for {\em all} distances. Additionally, we study
the weight distribution of Reed-Muller codes. Prior results of Kasami and
Tokura \cite{KT70} on the structure of Reed-Muller codewords up to twice the
minimum distance, imply bounds on the weight distribution of the code that
apply only until twice the minimum distance. We provide accumulative bounds for
the weight distribution of Reed-Muller codes that apply to {\em all} distances.

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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org