Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-06T10:49:06.407Z Has data issue: false hasContentIssue false

Sphere packings constructed from BCH and Justesen codes

Published online by Cambridge University Press:  26 February 2010

N. J. A. Sloane
Affiliation:
Bell Telephone Laboratories, Inc., Murray Hill, New Jersey, U.S.A.
Get access

Extract

Abstract. Bose-Chaudhuri-Hocquenghem and Justesen codes are used to pack equa spheres in n–dimensional Euclidean space with density Δ satisfying

for all sufficiently large n of the form m 2m, where m is a power of 4. These appear to be the densest packings yet constructed in high dimensional space.

Type
Research Article
Copyright
Copyright © University College London 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Berlekamp, E. R., Algebraic Coding Theory (McGraw-Hill, New York, 1968).Google Scholar
2.Justesen, J., “A class of constructive asymptotically good algebraic codes”, IEEE Trans. Information Theory, 18 (1972), 652656.CrossRefGoogle Scholar
3.Leech, J., “Notes on Sphere Packings”, Canadian J. Math., 19 (1967), 251267.CrossRefGoogle Scholar
4.Leech, J., and Sloane, N. J. A., “New Sphere Packings in Dimensions 9-15”, Bull. Amer. Math. Soc., 76 (1970), 10061010.CrossRefGoogle Scholar
5.Leech, J., and Sloane, N. J. A., “New Sphere Packings in More than Thirty-Two Dimensions”, Proc. 2nd Chapel Hill Conf. on a Combinatorial Mathematics and Its Applications (University of North Carolina at Chapel Hill, 1970), pp. 345355.Google Scholar
6.Leech, J., and Sloane, N. J. A., “Sphere Packings and Error-Correcting Codes”, Canadian J. Math., 23 (1971), 718745.CrossRefGoogle Scholar
7.Peterson, W. W., Error-Correcting Codes (M.I.T. Press, Cambridge, Mass., 1961), pp. 245247.Google Scholar
8.Rogers, C. A., Packings and Coverings (Cambridge University Press, Cambridge, 1964).Google Scholar