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An expander is a sparse (low degree) graph with high "expansion," measured in one of several ways; typically akin to the minimum ratio of the size of a subgraph boundary to the subgraph's volume.
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Are all linear-rate and -distance classical linear codes expanding?
Really cool question! This is a little bit on the handwavy side of things, but here is my take. The conclusion is that we can show the existence of an $\Omega(1)$-expander of size $\Theta(n)$, let me …
2
votes
0
answers
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Small set expansion and expanders
Given a graph $G=(V,E)$ on $n$ vertices and $0 \leq \delta \leq 1/2$, we can define the expansion of $G$ over small sets:
$$
h(G,\delta)= \min_{\vert S\vert \leq \delta n } \phi(S) \ ,
$$
with
$$\phi( …