Publication Date


Document Type


Committee Members

K. T. Arasu (Committee Chair), Yuqing Chen (Committee Member), Xiaoyu Liu (Committee Member)

Degree Name

Master of Science (MS)


Multilevel Hadamard Matrices (MHMs) have been examined by Trihn, Fan, and Gabidulin for constructions of multilevel zero-correlation zone sequences, which in turn have useful application in quasi-synchronous code division multiple access (CDMA) systems. Subsequently, Adams, Crawford, Greeley, Lee and Murugan introduced a construction of full-rate circulant MHMs and proved the existence of an order n MHM with n elements of distinct absolute value for all n, thus determining the maximum number of distinct elements permissible in an order n MHM to be the greatest possible. We give a survey of MHMs, in particular examining the circulant case and the methods for studying such objects. We provide several observations regarding Adams' construction, discuss the characterization of circulant matrices H satisfying HHT = wI for orders 3 and 4, and give new constructions for other orders of MHMs.

Page Count


Department or Program

Department of Mathematics and Statistics

Year Degree Awarded