Name
Abstract | ||
|---|---|---|
Abstract. Let S\subset[-1,1) . A finite set \Ccal=\set x
i
i=1
M
\subset\Re
n
is called a spherical S-code if \norm x
i
=1 for each i , and x
i
\tran x
j
∈ S , i\ne j . For S=[-1, 0.5] maximizing M=|C| is commonly referred to as the kissing number problem. A well-known technique based on harmonic analysis and linear programming can be used to bound M . We consider a modification of the bounding procedure that is applicable to antipodal codes; that is, codes where x∈\Ccal\implies -x∈\Ccal . Such codes correspond to packings of lines in the unit sphere, and include all codes obtained as the collection of minimal
vectors in a lattice. We obtain improvements in upper bounds for kissing numbers attainable by antipodal codes in dimensions
16≤ n≤ 23 . We also show that for n=4 , 6 and 7 the antipodal codes with maximal kissing numbers are essentially unique, and correspond to the minimal vectors
in the laminated lattices \Lam
n
.
|
Year | DOI | Venue |
|---|---|---|
2002 | 10.1007/s00454-001-0080-5 | Discrete & Computational Geometry |
Keywords | Field | DocType |
upper bound,harmonic analysis,linear program | Discrete mathematics,Topology,Combinatorics,Essentially unique,Finite set,Lattice (order),Linear programming,Antipodal point,Kissing number problem,Mathematics,Unit sphere | Journal |
Volume | Issue | ISSN |
28 | 1 | 0179-5376 |
Citations | PageRank | References |
2 | 1.04 | 2 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kurt M. Anstreicher | 1 | 633 | 86.40 |