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

Takuya Ikuta, Akihiro Munemasa

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalSpecial Matrices
Volume6
Issue number1
DOIs
Publication statusPublished - 2018 Jan 1

Keywords

  • Galois ring
  • association scheme
  • complex Hadamard matrix

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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