New upper bounds on sphere packings I
Copyright policy )New upper bounds on sphere packings I
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
26 pages, 1 figure
- Harvard University United States
- Microsoft (United States) United States
Mathematics - Metric Geometry, sphere packing, error-correcting code, Linear programming, FOS: Mathematics, Packing and covering in \(n\) dimensions (aspects of discrete geometry), linear programming bound, Metric Geometry (math.MG), Error probability in coding theory
Mathematics - Metric Geometry, sphere packing, error-correcting code, Linear programming, FOS: Mathematics, Packing and covering in \(n\) dimensions (aspects of discrete geometry), linear programming bound, Metric Geometry (math.MG), Error probability in coding theory
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