Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New bounds of permutation codes under Hamming metric and Kendall's
  $\tau$-metric   Permutation codes are widely studied objects due to their numerous
applications in various areas, such as power line communications, block
ciphers, and the rank modulation scheme for flash memories. Several kinds of
metrics are considered for permutation codes according to their specific
applications. This paper concerns some improvements on the bounds of
permutation codes under Hamming metric and Kendall's $\tau$-metric
respectively, using mainly a graph coloring approach. Specifically, under
Hamming metric, we improve the Gilbert-Varshamov bound asymptotically by a
factor $n$, when the minimum Hamming distance $d$ is fixed and the code length
$n$ goes to infinity. Under Kendall's $\tau$-metric, we narrow the gap between
the known lower bounds and upper bounds. Besides, we also obtain some sporadic
results under Kendall's $\tau$-metric for small parameters.

22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol