Symmetric Bush-type generalized Hadamard matrices and association schemes

Mutually Unbiased Bush-type Hadamard Matrices and Association Schemes

It was shown by LeCompte, Martin, and Owens in 2010 that the existence of mutually unbiased Hadamard matrices and the identity matrix, which coincide with mutually unbiased bases, is equivalent to that of a Q-polynomial association scheme of class four which is both Q-antipodal and Q-bipartite. We prove that the existence of a set of mutually unbiased Bush-type Hadamard matrices is equivalent t...

SYMMETRIC BUSH-TYPE HADAMARD MATRICES OF ORDER 4m EXIST FOR ALL ODD m

Using reversible Hadamard difference sets, we construct symmetric Bush-type Hadamard matrices of order 4m4 for all odd integers m.

Jacket matrices constructed from Hadamard matrices and generalized Hadamard matrices

Quasi-Cyclic Generalized Hadamard Matrices

In this paper, we define quasi-cyclic(QC) generalized Hadamard matrices and balanced QC generalized Hadamard matrices. Then we propose a new construction method for QC generalized Hadamard matrices. The proposed matrices are constructed from the balanced optimal low correlation zone(LCZ) sequence set which has correlation value −1 within low correlation zone.

Tri-weight Codes and Generalized Hadamard Matrices

The existence is shown of a set of (p~ -1) generalized Hadamard matrices H(p, p~'~) of order p2'~, each of which is symmetric and regular. When normalized to become unitary matrices, they form a multiplicative group of order p'~, simply isomorphic to the additive group of GF(pm). The rows of these (p~ 1) matrices are shown to be the image, under the well-known isomorphic mapping relating the pt...