BCCB complex Hadamard matrices of order 9, and MUBs

• 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 F-9((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.

Subject headings

NATURVETENSKAP  -- Matematik -- Annan matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Other Mathematics (hsv//eng)

Keyword

Complex Hadamard

9 Dimensions

BCCB

Mutually unbiased

Publication and Content Type

ref (subject category)

art (subject category)