Matrix analysis
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
On designs in compact metric spaces and a universal bound on their size
Proceedings of the conference on Discrete metric spaces
A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces
Journal of Algebraic Combinatorics: An International Journal
Quantum computation and quantum information
Quantum computation and quantum information
Designs in Grassmannian Spaces and Lattices
Journal of Algebraic Combinatorics: An International Journal
On Weyl-Heisenberg orbits of equiangular lines
Journal of Algebraic Combinatorics: An International Journal
Equiangular lines, mutually unbiased bases, and spin models
European Journal of Combinatorics
Multiple-antenna signal constellations for fading channels
IEEE Transactions on Information Theory
Linear programming bounds for codes in grassmannian spaces
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
We introduce the concepts of complex Grassmannian codes and designs. Let $\mathcal{G}_{m,n}$ denote the set of m-dimensional subspaces of 驴 n : then a code is a finite subset of $\mathcal{G}_{m,n}$ in which few distances occur, while a design is a finite subset of $\mathcal{G}_{m,n}$ that polynomially approximates the entire set. Using Delsarte's linear programming techniques, we find upper bounds for the size of a code and lower bounds for the size of a design, and we show that association schemes can occur when the bounds are tight. These results are motivated by the bounds for real subspaces recently found by Bachoc, Bannai, Coulangeon and Nebe, and the bounds generalize those of Delsarte, Goethals and Seidel for codes and designs on the complex unit sphere.