Meyer, Annika2013-03-282013-03-282013-03-28201310.1007/s10623-012-9724-0https://infoscience.epfl.ch/handle/20.500.14299/91003WOS:000313056200025Let L be a lattice in . This paper provides two methods to obtain upper bounds on the number of points of L contained in a small sphere centered anywhere in . The first method is based on the observation that if the sphere is sufficiently small then the lattice points contained in the sphere give rise to a spherical code with a certain minimum angle. The second method involves Gaussian measures on L in the sense of Banaszczyk (Math Ann 296:625-635, 1993). Examples where the obtained bounds are optimal include some root lattices in small dimensions and the Leech lattice. We also present a natural decoding algorithm for lattices constructed from lattices of smaller dimension, and apply our results on the number of lattice points in a small sphere to conclude on the performance of this algorithm.LatticeSphere decodingSpherical codeKissing numberGaussian measureLattice decodingtext::journal::journal article::research article