Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4

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

Abstrakty

EN

We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.

Słowa kluczowe

EN

association scheme; complex Hadamard matrix; Galois ring

Kategorie tematyczne

• 05E30: Association schemes, strongly regular graphs

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2018
• Tom: 6
• Numer: 1
• Strony: 1-10

Daty

wydano

2018-01-01

otrzymano

2017-12-18

zaakceptowano

2017-12-18

online

2018-01-24

Twórcy

autor

Takuya Ikuta

• , 650-8586,

autor

Akihiro Munemasa

• , 980-8579,

Identyfikatory

DOI

10.1515/spma-2018-0001