Cretan(4t+1) Matrices

N. A. Balonin; Jennifer Seberry

paper

Cretan(4t+1) Matrices

arXiv:1510.05736

Abstract

A $C r e t an (4 t + 1)$ matrix, of order $4 t + 1$ , is an orthogonal matrix whose elements have moduli $\leq 1$ . The only $C r e t an (4 t + 1)$ matrices previously published are for orders 5, 9, 13, 17 and 37. This paper gives infinitely many new $C r e t an (4 t + 1)$ matrices constructed using $r e g u l a r H a d ama r d$ matrices, $S B I B D (4 t + 1, k, λ)$ , weighing matrices, generalized Hadamard matrices and the Kronecker product. We introduce an inequality for the radius and give a construction for a Cretan matrix for every order $n \geq 3$ .

16 pages, 7 figures