Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Bound on the Minimal Field Size of LRCs, and Cyclic MR Codes That
  Attain It   We prove a new lower bound on the field size of locally repairable codes
(LRCs). Additionally, we construct maximally recoverable (MR) codes which are
cyclic. While a known construction for MR codes has the same parameters, it
produces non-cyclic codes. Furthermore, we prove necessary and sufficient
conditions that specify when the known non-cyclic MR codes may be permuted to
become cyclic, thus proving our construction produces cyclic MR codes with new
parameters. Furthermore, using our new bound on the field size, we show that
the new cyclic MR codes have optimal field size in certain cases. Other known
LRCs are also shown to have optimal field size in certain cases.

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The categories of this paper are: cond-mat
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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: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph