… We show in this work that high dimensional expanders imply lattices with good distance.
There are … We show that high dimensional expanders can be used in order to construct …

… codes) [DK17], lattices with large distance [KM18], list-… a sufficiently good (one dimensional)
spectral expander, then … closure, is a sufficiently good (k − 1)-dimensional expander. …

… of the (d − 2)-dimensional faces in these complexes are good expander graphs. By Fact 2.9,
… beyond the square root distance barrier using high dimensional expanders. In Proceedings …

… , to obtain good symmetric LDPC codes that were previously based on Ramanujan graphs.
… an explicit construction of a binary symmetric code with constant rate and constant distance. …

… ϵ, ϵ-dimension expanders of arbitrarily large dimension. He … the complex numbers and
possibly over finite fields as well. … Then Γ sits diagonally as a lattice in the group of real points of …

… 1.1 for lattices in connected simple real Lie groups with high rank is obtained as well (see …
By replacing μ by a measure with finite support and at total variation distance less than 1 4 …

… To the best of our knowledge, all known hard instances, proving inapproximability in the
SoS … For two i-chains f, g, we define the distance between f and g to be dist(f, g) = |f + g|. …

… rapid mixing which allows both negative as well as positive correlations, so long as the total
… at each distance scale. The class of amenable graphs notably includes lattices such as Zd …

… by both the complete complex as well as high-dimensional expanders. We show that the
results … An important example is the Grassmann lattice of all subspaces of a finite-dimensional …

… that come from high-dimensional expanders, in particular … that have a large X-distance
but a much smaller Z-distance. … LSV complexes, but good quantum codes are also liable to …