Sphere Packings and Error-Correcting Codes

Error-correcting codes are used in several constructions for packings of equal spheres in n -dimensional Euclidean spaces E n . These include a systematic derivation of many of the best sphere packings known, and construction of new packings in dimensions 9-15, 36, 40, 48, 60, and 2 m for m ≧ 6. Most of the new packings are nonlattice packings. These new packings increase the previously greatest known numbers of spheres which one sphere may touch, and, except in dimensions 9, 12, 14, 15, they include denser packings than any previously known. The density Δ of the packings in E n for n = 2 m satisfies In this paper we make systematic use of error-correcting codes to obtain sphere packings in E n , including several of the densest packings known and several new packings.