Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Bounds on the Rate of Locally Repairable Codes   New asymptotic upper bounds are presented on the rate of sequences of locally
repairable codes (LRCs) with a prescribed relative minimum distance and
locality over a finite field $F$. The bounds apply to LRCs in which the
recovery functions are linear; in particular, the bounds apply to linear LRCs
over $F$. The new bounds are shown to improve on previously published results,
especially when the repair groups are disjoint, namely, they form a partition
of the set of coordinates.

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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an