A complex Hadamard matrix of order 94

TL;DR

This paper presents a novel construction of a complex Hadamard matrix of order 94 by modifying existing block construction methods and utilizing computer-aided discovery of circulant matrices of order 47.

Contribution

It introduces a new method to construct complex Hadamard matrices of order 2p using circulant matrices, with the first known example for order 94.

Findings

Constructed a complex Hadamard matrix of order 94 for the first time.

Developed a modified block construction method.

Used computer-aided techniques to identify necessary circulant matrices.

Abstract

In this paper we modify a fundamental block construction of Kharaghani and Seberry and show how to use certain circulant $\{-1,1\}$-matrices of odd order $p$ to construct a complex Hadamard matrix of order $2p$. In particular, for $p=47$ we use computer-aided methods to discover the necessary circulant matrices, and consequently give a construction of a complex Hadamard matrix of order $94$ for the first time.