Necessary conditions for the existence of group-invariant Butson Hadamard matrices and a new family of perfect arrays

• Main Author: Duc, Tai Do
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2020
• Subjects: Science::Mathematics; Group Invariant Butson Hadamard Matrices; Perfect Arrays
• Online Access: https://hdl.handle.net/10356/143067
• Institution: Nanyang Technological University

Let G be a finite abelian group and let exp (G) denote the least common multiple of the orders of all elements of G. A BH(G,h) matrix is a G-invariant | G| × | G| matrix H whose entries are complex hth roots of unity such that HH∗= | G| I|G|. By νp(x) we denote the p-adic valuation of the integer x....