2008/06/13 by Aidan Roy, Roy, Aidan · 2 citations
Computer Science · Engineering · Mathematics · #94B27 #94B65 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.0806.2317
openalex publication_date 2008/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the concepts of complex Grassmannian codes and designs. Let G(m,n) denote the set of m-dimensional subspaces of Cn: 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.