Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Generic Transformation to Generate MDS Storage Codes with
  $\delta$-Optimal Access Property   For high-rate maximum distance separable (MDS) codes, most of them are
designed to optimally repair a single failed node by connecting all the
surviving nodes. However, in practical systems, sometimes not all the surviving
nodes are available. To facilitate the practical storage system, a few
constructions of $(n,k)$ MDS codes with the property that any single failed
node can be optimally repaired by accessing any $d$ surviving nodes have been
proposed, where $d\in [k+1:n-1)$. However, all of them either have large
sub-packetization levels or are not explicit for all the parameters. To address
these issues, we propose a generic transformation that can convert any
$(n',k')$ MDS code to another $(n,k)$ MDS code with the optimal repair property
and optimal access property for an arbitrary set of two nodes, while the repair
efficiency of the remaining $n-2$ nodes can be kept. By recursively applying
the generic transformation to a scalar MDS code multiple times, we get an MDS
code with the optimal repair property and the optimal access property for all
nodes, which outperforms previous known MDS codes in terms of either the
sub-packetization level or the flexibility of the parameters.

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The categories of this paper are: comp-gas
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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: eess
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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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: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con