Codes and designs in Grassmannian spaces
| Autor: | Christine Bachoc, Renaud Coulangeon, Eiichi Bannai |
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| Rok vydání: | 2004 |
| Předmět: |
Discrete mathematics
Algebraic combinatorics Duality (mathematics) Space (mathematics) Upper and lower bounds Group representation Codes Theoretical Computer Science Combinatorics Square-integrable function Bounds Designs Zonal functions Grassmannian Discrete Mathematics and Combinatorics Orthogonal group Grassmann manifold Mathematics |
| Zdroj: | Discrete Mathematics. 277:15-28 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/s0012-365x(03)00151-1 |
| Popis: | The notion of t-design in a Grassmannian space G"m","n was introduced by the first and last authors and G. Nebe in a previous paper. In the present work, we give a general lower bound for the size of such designs. The method is inspired by Delsarte, Goethals and Seidel work in the case of spherical designs. This leads us to introduce a notion of f-code in Grassmannian spaces, for which we obtain upper bounds, as well as a kind of duality tight-designs/tight-codes. The bounds are in terms of the dimensions of the irreducible representations of the orthogonal group O(n) occurring in the decomposition of the space L^2(G"m","n^o) of square integrable functions on G"m","n^o, the set of oriented Grassmanianns. |
| Databáze: | OpenAIRE |
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