Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of optimal locally repairable codes via automorphism groups
  of rational function fields   Locally repairable codes, or locally recoverable codes (LRC for short) are
designed for application in distributed and cloud storage systems. Similar to
classical block codes, there is an important bound called the Singleton-type
bound for locally repairable codes. In this paper, an optimal locally
repairable code refers to a block code achieving this Singleton-type bound.
Like classical MDS codes, optimal locally repairable codes carry some very nice
combinatorial structures. Since introduction of the Singleton-type bound for
locally repairable codes, people have put tremendous effort on constructions of
optimal locally repairable codes. Due to hardness of this problem, there are
few constructions of optimal locally repairable codes in literature. Most of
these constructions are realized via either combinatorial or algebraic
structures.
  In this paper, we employ automorphism groups of rational function fields to
construct optimal locally repairable codes by considering the group action on
the projective lines over finite fields. It turns out that we are able to
construct optimal locally repairable codes with reflexibility of locality as
well as smaller alphabet size comparable to the code length. In particular, we
produce new families of $q$-ary locally repairable codes, including codes of
length $q+1$ via cyclic groups and codes via dihedral groups.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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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: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg