Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Optimal Minimum Distance of Fractional Repetition Codes   Fractional repetition (FR) codes are a class of repair efficient erasure
codes that can recover a failed storage node with both optimal repair bandwidth
and complexity. In this paper, we study the minimum distance of FR codes, which
is the smallest number of nodes whose failure leads to the unrecoverable loss
of the stored file. We consider upper bounds on the minimum distance and
present several families of explicit FR codes attaining these bounds. The
optimal constructions are derived from regular graphs and combinatorial
designs, respectively.

9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat