Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sidon Sets, Difference Sets, and Codes in $ A_n $ Lattices   This chapter investigates the properties of (linear) codes in $ A_n $
lattices, the practical motivation for which is found in several communication
scenarios, such as asymmetric channels, sticky-insertion channels, bit-shift
channels, and permutation channels. In particular, a connection between these
codes and notions of difference sets and Sidon sets in Abelian groups is
demonstrated. It is shown that the $ A_n $ lattice admits a linear perfect code
of radius $ 1 $ if and only if there exists an Abelian planar difference set of
cardinality $ n + 1 $. Similarly, a direct link is given between linear codes
of radius $ r $ in the $ A_n $ lattice and Sidon sets of order $ 2r $ and
cardinality $ n + 1 $. Sidon sets of order $ 2r-1 $ are also represented
geometrically in a similar way. Apart from providing geometric intuition about
Sidon sets, this interpretation enables simple derivations of bounds on their
parameters, which are either equivalent to, or improve upon the known bounds.
In connection to the above, more general (non-planar) Abelian difference sets
and perfect codes of radius $ r $ are also discussed.

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The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci