-reducible complex Hadamard matrices of order 6

✍ Scribed by Bengt R. Karlsson

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 160 KB
• Volume: 434
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.08.021

✦ Synopsis

Complex Hadamard matrices H of order 6 are characterized in a novel manner, according to the presence/absence of order 2 Hadamard submatrices. It is shown that if there exists one such submatrix, H is equivalent to a Hadamard matrix where all the nine submatrices are Hadamard. The ensuing subset of H 2reducible complex Hadamard matrices is more general than might be thought, and, significantly, includes all the up till now described (one-and two-parameter) families of order 6. A known, isolated matrix, and most numerically generated matrices, fall outside the subset.