Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Locally Repairable and Secure Codes for Distributed Storage
  Systems   This paper aims to go beyond resilience into the study of security and
local-repairability for distributed storage systems (DSS). Security and
local-repairability are both important as features of an efficient storage
system, and this paper aims to understand the trade-offs between resilience,
security, and local-repairability in these systems. In particular, this paper
first investigates security in the presence of colluding eavesdroppers, where
eavesdroppers are assumed to work together in decoding stored information.
Second, the paper focuses on coding schemes that enable optimal local repairs.
It further brings these two concepts together, to develop locally repairable
coding schemes for DSS that are secure against eavesdroppers.
  The main results of this paper include: a. An improved bound on the secrecy
capacity for minimum storage regenerating codes, b. secure coding schemes that
achieve the bound for some special cases, c. a new bound on minimum distance
for locally repairable codes, d. code construction for locally repairable codes
that attain the minimum distance bound, and e. repair-bandwidth-efficient
locally repairable codes with and without security constraints.

7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph