# Balancedly splittable Hadamard matrices

@article{Kharaghani2019BalancedlySH, title={Balancedly splittable Hadamard matrices}, author={Hadi Kharaghani and Sho Suda}, journal={Discret. Math.}, year={2019}, volume={342}, pages={546-561} }

Balancedly splittable Hadamard matrices are introduced and studied. A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased Hadamard matrices. Several construction methods are presented. As an application, commutative association schemes of 4, 5, and 6 classes are constructed.

## 4 Citations

Weakly Hadamard diagonalizable graphs

- Mathematics
- 2021

Abstract A matrix is called weakly Hadamard if its entries are from { 0 , − 1 , 1 } and its non-consecutive columns (with some ordering) are orthogonal. Unlike Hadamard matrices, there is a weakly…

Balancedly splittable orthogonal designs and equiangular tight frames

- Computer Science, MathematicsDes. Codes Cryptogr.
- 2021

The concept of balancedly splittable orthogonal designs is introduced along with a recursive construction. As an application, equiangular tight frames over the real, complex, and quaternions meeting…

Complex Hadamard diagonalisable graphs

- Mathematics, Physics
- 2020

In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex Hadamard matrices.…

Hadamard diagonalizable graphs of order at most 36

- Mathematics
- 2020

If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries $\pm1$, then the matrix formed by taking the columns as the eigenvectors is a Hadamard matrix and the graph…

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