Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Quaternary (r,delta)-Locally Repairable Codes Achieving the
  Singleton-type Bound   Locally repairable codes enables fast repair of node failure in a distributed
storage system. The code symbols in a codeword are stored in different storage
nodes, such that a disk failure can be recovered by accessing a small fraction
of the storage nodes. The number of storage nodes that are contacted during the
repair of a failed node is a parameter called locality. We consider locally
repairable codes that can be locally recovered in the presence of multiple node
failures. The punctured code obtained by removing the code symbols in the
complement of a repair group is called a local code. We aim at designing a code
such that all local codes have a prescribed minimum distance, so that any node
failure can be repaired locally, provided that the total number of node
failures is less than the tolerance parameter. We consider linear locally
repairable codes defined over a finite field of size four. This alphabet has
characteristic 2, and hence is amenable to practical implementation. We
classify all quaternary locally repairable codes that attain the Singleton-type
upper bound for minimum distance. For each combination of achievable code
parameters, an explicit code construction is given.

10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex