H. Kharaghani

activity

20122022

collaborators

12 papers

math.CO2022

Hadamard matrices related to the projective planes

Hadi Kharaghani, Sho Suda

Let $n$ be the order of a (quaternary) Hadamard matrix. It is shown that the existence of a projective plane of order $n$ is equivalent to the existence of a balancedly multi-split…

math.CO2022

Quasi-balanced weighing matrices, signed strongly regular graphs and association schemes

Hadi Kharaghani, Thomas Pender, Sho Suda

A weighing matrix $W$ is quasi-balanced if $∣ W ∣∣ W ∣^{⊤} = ∣ W ∣^{⊤} ∣ W ∣$ has at most two off-diagonal entries, where $∣ W ∣_{ij} = ∣ W_{ij} ∣$ . A quasi-balanced weighing matrix $W$ signs a s…

math.CO2021

Balanced Weighing Matrices

Hadi Kharaghani, Thomas Pender, Sho Suda

A unified approach to the construction of weighing matrices and certain symmetric designs is presented. Assuming the weight $p$ in a weighing matrix $W (n, p)$ is a prime power, it i…

math.CO2021

A family of balanced generalized weighing matrices

Hadi Kharaghani, Thomas Pender, Sho Suda

Balanced weighing matrices with parameters $(1 + 18 \cdot \frac{9 ^{m + 1} - 1}{8}, 9^{m + 1}, 4 \cdot 9^{m}),$ for each nonzero integer $m$ is constructed. This is the first infini…

math.CO2020

Divisible design digraphs and association schemes

Hadi Kharaghani, Sho Suda

Divisible design digraphs are constructed from skew balanced generalized weighing matrices and generalized Hadamard matrices. Commutative and non-commutative association schemes ar…

math.CO2020

Disjoint weighing matrices

Hadi Kharaghani, Sho Suda, Behruz Tayfeh-Rezaie

The notion of disjoint weighing matrices is introduced as a generalization of orthogonal designs. A recursive construction along with a computer search lead to some infinite classe…