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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
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Binary codes with upper and lower bound on pairwise distance
The Gilbert-Varshamov bound provides a lower bound for codes of length $n$ with minimum pairwise distance (say $\frac{n}8$). If we wish for the codes to also have pairwise distances bounded above (say …