Bounds for discrepancies in the Hamming space
Metric Geometry
2020-08-31 v2 Information Theory
math.IT
Abstract
We derive bounds for the ball -discrepancies in the Hamming space for and . Sharp estimates of discrepancies have been obtained for many spaces such as the Euclidean spheres and more general compact Riemannian manifolds. In the present paper, we show that the behavior of discrepancies in the Hamming space differs fundamentally because the volume of the ball in this space depends on its radius exponentially while such a dependence for the Riemannian manifolds is polynomial.
Cite
@article{arxiv.2007.09721,
title = {Bounds for discrepancies in the Hamming space},
author = {Alexander Barg and Maxim Skriganov},
journal= {arXiv preprint arXiv:2007.09721},
year = {2020}
}