Coset code constructions of N-dimensional sphere packings from 1- and 2-dimensional lattices

Abstract

A technique for constructing N-dimensional sphere packings from certain one- and two-dimensional lattices is described. The packings are constructed as coset codes and take advantage of partitions of the base lattices that result in Hamming spaces. Known Hamming metric codes over GF(2), GF(3), GF(5), and GF(7) are used in the construction. The resulting packings are compared with the best known packings in each dimension. At low dimensions, many of these packings are the densest known; as the dimension increases, however, the packings become inferior to the best known ones.<>