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

Takuya Ikuta, Akihiro Munemasa

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1-10
ページ数10
ジャーナルSpecial Matrices
6
1
DOI
出版ステータスPublished - 2018 1月 1

ASJC Scopus subject areas

  • 代数と数論
  • 幾何学とトポロジー

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