Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rate-distance tradeoff for codes above graph capacity   The capacity of a graph is defined as the rate of exponential growth of
independent sets in the strong powers of the graph. In the strong power an edge
connects two sequences if at each position their letters are equal or adjacent.
We consider a variation of the problem where edges in the power graphs are
removed between sequences which differ in more than a fraction $\delta$ of
coordinates. The proposed generalization can be interpreted as the problem of
determining the highest rate of zero undetected-error communication over a link
with adversarial noise, where only a fraction $\delta$ of symbols can be
perturbed and only some substitutions are allowed.
  We derive lower bounds on achievable rates by combining graph homomorphisms
with a graph-theoretic generalization of the Gilbert-Varshamov bound. We then
give an upper bound, based on Delsarte's linear programming approach, which
combines Lov\'asz' theta function with the construction used by McEliece et al.
for bounding the minimum distance of codes in Hamming spaces.

34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con