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A complex Hadamard matrix of order 94

Ferenc Szöllősi

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.

A complex Hadamard matrix of order 94

Abstract

In this paper we modify a fundamental block construction of Kharaghani and Seberry and show how to use certain circulant -matrices of odd order to construct a complex Hadamard matrix of order . In particular, for we use computer-aided methods to discover the necessary circulant matrices, and consequently give a construction of a complex Hadamard matrix of order for the first time.
Paper Structure (3 sections, 9 theorems, 13 equations)

This paper contains 3 sections, 9 theorems, 13 equations.

Table of Contents

  1. Introduction and main results
  2. The Goethels--Seidel array and complex Hadamard matrices
  3. The search for circulant matrices of order $47$

Key Result

Theorem 1

There exists a complex Hadamard matrix of order $94$.

Theorems & Definitions (16)

  • Theorem 1
  • Theorem 2: GSA
  • Lemma 1
  • Lemma 2
  • proof
  • Theorem 3: DJgood, KS
  • Lemma 3
  • proof
  • Theorem 4
  • proof
  • ...and 6 more