Constructions of complex Hadamard matrices using Algebraic Combinatorics and its applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400215
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kobe Gakuin University
• Principal Investigator: Ikuta Takuya 神戸学院大学, 法学部, 教授 (70271111)
• Co-Investigator(Kenkyū-buntansha): MUNEMASA AKIHIRO 東北大学, 大学院情報科学研究科, 教授 (50219862)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 複素アダマール行列 / type-II行列 / アソシエーション・スキーム / Bose-Mesner代数 / 野村代数

Outline of Final Research Achievements

The aim of this research is to construct infinite series of complex Hadamard matrices, and more generally, type-II matrices, in the Bose--Mesner algebra of a certain 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.

Free Research Field

代数的組合せ論