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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.

2 votes

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 …
loplo's user avatar
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2 votes
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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( …
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