@article{Kharaghani2019BalancedlySH,
journal={Discret. Math.},
year={2019},
volume={342},
pages={546-561}
}
• Published 1 June 2018
• Mathematics, Computer Science
• Discret. Math.
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

## Tables and Topics from this paper

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, Mathematics
Des. 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
• 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
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

## References

SHOWING 1-10 OF 34 REFERENCES
Doubly Regular Tournaments are Equivalent to Skew Hadamard Matrices
• Computer Science, Mathematics
J. Comb. Theory, Ser. A
• 1972
Doubly regular tournaments and homogeneous tournaments are defined and shown to be equivalent and existence of such a tournament is equivalent to the existence of a skew Hadamard matrix of order n + 1.
On a class of quaternary complex Hadamard matrices
• Mathematics, Computer Science
Discret. Math.
• 2018
A class of regular unit Hadamard matrices whose entries consist of two complex numbers and their conjugates for a total of four complex numbers are introduced and contained in the Bose-Mesner algebra of an association scheme arising from skew Paley matrices.
Hoffman's coclique bound for normal regular digraphs, and nonsymmetric association schemes
• Mathematics
• 2015
We extend Hoffman's coclique bound for regular digraphs with the property that its adjacency matrix is normal, and discuss cocliques attaining the inequality. As a consequence, we characterize
• Mathematics
• 2011
Of interest here is a characterization of the undirected graphs G such that the Laplacian matrix associated with G can be diagonalized by some Hadamard matrix. Many interesting and fundamental
Linked systems of symmetric group divisible designs of type II
• Mathematics, Computer Science
Des. Codes Cryptogr.
• 2019
Linked systems of symmetric group divisible designs of type II are introduced, and several examples are obtained from affine resolvable designs and a variant of mutually orthogonal Latin squares.
The excess problem and some excess inequivalent matrices of order 32
• Mathematics
• 1998
Abstract Let 4 n be the order of an Hadamard matrix. It is shown that there is a regular complex Hadamard matrix of order 8 n 2 . Five classes of excess-inequivalent Hadamard matrices of order 32 are
Linked systems of symmetric group divisible designs
• Mathematics
• 2016
We introduce the concept of linked systems of symmetric group divisible designs. The connection with association schemes is established, and as a consequence we obtain an upper bound on the number of
3-Class Association Schemes and Hadamard Matrices of a Certain Block Form
• Computer Science, Mathematics
Eur. J. Comb.
• 1998
All Hadamard matrices of this form are constructed in which all blocksHij have rank 1 and Jg = JgHij =-0.