A note on the existence of BH(19,6) matrices

TL;DR

This paper demonstrates the existence of a specific complex Hadamard matrix of order 19 with sixth roots of unity using a block construction method.

Contribution

It provides a new explicit example of a BH(19,6) matrix, expanding the known classes of complex Hadamard matrices.

Findings

Existence of a BH(19,6) matrix confirmed

Constructed using Petrescu's block approach

Advances understanding of complex Hadamard matrices

Abstract

In this note we utilize a non-trivial block approach due to M. Petrescu to exhibit a Butson-type complex Hadamard matrix of order 19, composed of sixth roots of unity.