Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally Repairable Codes with Functional Repair and Multiple Erasure
  Tolerance   We consider the problem of designing [n; k] linear codes for distributed
storage systems (DSS) that satisfy the (r, t)-Local Repair Property, where any
t'(<=t) simultaneously failed nodes can be locally repaired, each with locality
r. The parameters n, k, r, t are positive integers such that r<k<n and t <=
n-k. We consider the functional repair model and the sequential approach for
repairing multiple failed nodes. By functional repair, we mean that the packet
stored in each newcomer is not necessarily an exact copy of the lost data but a
symbol that keep the (r, t)-local repair property. By the sequential approach,
we mean that the t' newcomers are ordered in a proper sequence such that each
newcomer can be repaired from the live nodes and the newcomers that are ordered
before it. Such codes, which we refer to as (n, k, r, t)-functional locally
repairable codes (FLRC), are the most general class of LRCs and contain several
subclasses of LRCs reported in the literature.
  In this paper, we aim to optimize the storage overhead (equivalently, the
code rate) of FLRCs. We derive a lower bound on the code length n given t
belongs to {2,3} and any possible k, r. For t=2, our bound generalizes the rate
bound proved in [14]. For t=3, our bound improves the rate bound proved in
[10]. We also give some onstructions of exact LRCs for t belongs to {2,3} whose
length n achieves the bound of (n, k, r, t)-FLRC, which proves the tightness of
our bounds and also implies that there is no gap between the optimal code
length of functional LRCs and exact LRCs for certain sets of parameters.
Moreover, our constructions are over the binary field, hence are of interest in
practice.

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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph