Bounds for codes and designs in complex subspaces

Details Bounds for codes and designs in complex subspaces Bounds for codes and designs in complex subspaces

2008-06-13

arxiv.org/abs/0806.2317v1

Mathematics

Combinatorics

33 pages, no figures

Scientific paper

We introduce the concepts of complex Grassmannian codes and designs. Let G(m,n) denote the set of m-dimensional subspaces of C^n: then a code is a finite subset of G(m,n) in which few distances occur, while a design is a finite subset of 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, Coulangeon and Nebe, and the bounds generalize those of Delsarte, Goethals and Seidel for codes and designs on the complex unit sphere.

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