Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On MBR codes with replication   An early paper by Rashmi et. al. presented the construction of an
$(n,k,d=n-1)$ MBR regenerating code featuring the inherent double replication
of all code symbols and repair-by-transfer (RBT), both of which are important
in practice. We first show that no MBR code can contain even a single code
symbol that is replicated more than twice. We then go on to present two new
families of MBR codes which feature double replication of all systematic
message symbols. The codes also possess a set of $d$ nodes whose contents
include the message symbols and which can be repaired through help-by-transfer
(HBT). As a corollary, we obtain systematic RBT codes for the case $d=(n-1)$
that possess inherent double replication of all code symbols and having a field
size of $O(n)$ in comparison with the general, $O(n^2)$ field size requirement
of the earlier construction by Rashmi et. al. For the cases $(k=d=n-2)$ or
$(k+1=d=n-2)$, the field size can be reduced to $q=2$, and hence the codes can
be binary. We also give a necessary and sufficient condition for the existence
of MBR codes having double replication of all code symbols and also suggest
techniques which will enable an arbitrary MBR code to be converted to one with
double replication of all code symbols.

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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: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-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: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess