On Generalizing the Method of Scarpis to Complex Hadamard Matrices

A complex Hadamard matrix is a matrix \(H_n ∈ {\{ω^i | 1≤ i ≤ m \}}n× n\) of order \(n\), where \(ω\) is a primitive \(mᵗʰ\) root of unity, that satisfies \(H_n{H}*_n=n{Iₙ}\), where \(H_n*\) denotes the complex conjugate transpose of \(H_n\). We show that the Scarpis technique for constructing classic Hadamard matrices generalizes to Butson-type complex Hadamard matrices.