University of Isfahan Transactions on Combinatorics 2251-8657 13 1 2024 03 01 Hadamard matrices of composite orders 31 40 27062 10.22108/toc.2022.133659.1989 EN Tianbing Xia School of Computing and Information Technology, University of Wollongong Australia, Wollongong, Australia Guoxin Zuo School of Mathematics and Statistics, Central China Normal University, Wuhan, China Liantang Lou College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, China Mingyuan Xia School of Mathematics and Statistics, Central China Normal University, Wuhan, China Journal Article 2022 05 15 In this paper, we give a method for the constructions of Hadamard matrices of composite orders by using suitable $T$-matrices and known Hadamard matrices. We establish a formula for $T$-matrices and Hadamard matrices and discuss under what condition we can get $T$-matrices from the known Hadamard matrices. Composite Hadamard matrix $T$-matrix Hadamard matrix Suitable matrices https://toc.ui.ac.ir/article_27062_c8e585f002d7d36b07ebc0cab4ddbe16.pdf