Linear programming bounds for codes in Grassmannian spaces
arXiv:math/0610812 · doi:10.1109/TIT.2006.872973
Abstract
We introduce a linear programming method to obtain bounds on the cardinality of codes in Grassmannian spaces for the chordal distance. We obtain explicit bounds, and an asymptotic bound that improves on the Hamming bound. Our approach generalizes the approach originally developed by P. Delsarte and Kabatianski-Levenshtein for compact two-point homogeneous spaces.
35 pages, 1 figure
References in corpus (1)
Cited by in corpus (24)
- Unitary designs and codes
- Optimal simplices and codes in projective spaces
- Tight p-fusion frames
- Invariant semidefinite programs
- Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps
- Lower bounds for measurable chromatic numbers
- Signal reconstruction from the magnitude of subspace components
- Three-point bounds for energy minimization
- Semidefinite programming, harmonic analysis and coding theory
- Quasi Monte Carlo integration and kernel-based function approximation on Grassmannians
- A bound on Grassmannian codes
- Lecture notes: Semidefinite programs and harmonic analysis
- Spectral approach to linear programming bounds on codes
- Moments of isotropic measures and optimal projective codes
- Bounds for codes and designs in complex subspaces
- Bounds on ordered codes and orthogonal arrays
- Maximal Orthoplectic Fusion Frames from Mutually Unbiased Bases and Block Designs
- Kerdock Codes for Limited Feedback Precoded MIMO Systems
- Linear programming bounds for regular graphs
- Semidefinite programming bounds for error-correcting codes
- A functional view of upper bounds on codes
- Linear Programming Bounds
- Applications of semidefinite programming to coding theory
- Bounds for codes in products of spaces, Grassmann and Stiefel manifolds