2016/04/13 by Bengt R. Karlsson
Engineering · Mathematics · Physics and Astronomy · #Advanced Photonic Communication Systems #Affine transformation #Block (permutation group theory) #Circulant matrix #Combinatorics #Complex Hadamard matrix #Dimension (graph theory) #Hadamard matrix #Hadamard transform #Hadamard's maximal determinant problem #Intersection (aeronautics) #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Optical Network Technologies #Orbit (dynamics) #Order (exchange) #Pure mathematics #Type (biology) #graph theory and CDMA systems #quant-ph
paper · pdf · doi:10.1016/j.laa.2016.04.012
published as Linear Algebra Appl., 504 (2016), pp. 309-324 · 14 pages, 3 figures
arxiv created 2016/04/13 · arxiv updated 2016/04/21 · openalex publication_date 2016/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A new type of complex Hadamard matrices of order 9 are constructed. The studied matrices are symmetric, block circulant with circulant blocks (BCCB) and form an until now unknown non-reducible and non-affine two-parameter orbit. Several suborbits are identified, including a one-parameter intersection with the Fourier orbit F9(4). The defect of this new type of Hadamard matrices is observed to vary, from a generic value 2 to the anomalous values 4 and 10 for some sub-orbits, and to 12 and 16 for some single matrices. The latter matrices are shown to be related to complete sets of MUBs in dimension 9.