Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Average-radius list-recovery of random linear codes: it really ties the
  room together   We analyze the list-decodability, and related notions, of random linear
codes. This has been studied extensively before: there are many different
parameter regimes and many different variants. Previous works have used
complementary styles of arguments---which each work in their own parameter
regimes but not in others---and moreover have left some gaps in our
understanding of the list-decodability of random linear codes. In particular,
none of these arguments work well for list-recovery, a generalization of
list-decoding that has been useful in a variety of settings.
  In this work, we present a new approach, which works across parameter regimes
and further generalizes to list-recovery. Our main theorem can establish better
list-decoding and list-recovery results for low-rate random linear codes over
large fields; list-recovery of high-rate random linear codes; and it can
recover the rate bounds of Guruswami, Hastad, and Kopparty for constant-rate
random linear codes (although with large list sizes).

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph