Complex Hadamard Matrices contained in a Bose–Mesner algebra

• Autorzy: Takuya Ikuta , Akihiro Munemasa
• Języki publikacji: EN

Abstrakty

EN

Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric association scheme. In particular, we recover the complex Hadamard matrices of order 15 found by Ada Chan. We compute the Haagerup sets to show inequivalence of resulting type-II matrices, and determine the Nomura algebras to show that the resulting matrices are not decomposable into generalized tensor products.

Słowa kluczowe

EN

association scheme; complex Hadamard matrix; type-II matrix

Kategorie tematyczne

• 05E30: Association schemes, strongly regular graphs

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2014-11-21

zaakceptowano

2015-04-22

online

2015-05-07

Twórcy

autor

Takuya Ikuta

• Kobe Gakuin University, Kobe, 650-8586, Japan

autor

Akihiro Munemasa

• Tohoku University, Sendai, 980-8579, Japan,

Bibliografia

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Identyfikatory

DOI

10.1515/spma-2015-0009