Journal article
Improved Linear Programming Bounds for Antipodal Spherical Codes
Discrete & computational geometry, Vol.28(1), pp.107-114
07/01/2002
DOI: 10.1007/s00454-001-0080-5
Abstract
Let S ⊂ [-1,1). A finite set C={xi}Mi=1⊂Rn is called a spherical S-code if ∥x i ∥ =1 for each i, and x T i x j ∈ S, i ≠ 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∈C⇒−x∈C
. 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 Λ n .
Details
- Title: Subtitle
- Improved Linear Programming Bounds for Antipodal Spherical Codes
- Creators
- Kurt M Anstreicher - Industrial and Systems Engineering
- Resource Type
- Journal article
- Publication Details
- Discrete & computational geometry, Vol.28(1), pp.107-114
- DOI
- 10.1007/s00454-001-0080-5
- ISSN
- 0179-5376
- eISSN
- 1432-0444
- Language
- English
- Date published
- 07/01/2002
- Academic Unit
- Business Analytics; Industrial and Systems Engineering; Computer Science
- Record Identifier
- 9984380389502771
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