Multilevel Hadamard Matrices

Abstract

<p>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-synchronus code division multiple access (COMA) systems. Subsequently, Adams, Crawford, Greeley, Lee and Murugan introduced a construction of full-rate circulant MHMs that proved the existence of an order n MHM with n elements of distinct absolute value for all n. We examine MHMs and the family of full-rate circulant MHMs (FCMHMs) introduced by the construction of Adams et al. and explain the existence of other forms of FCMHMs by means of new constructions.</p><p>This presentation occurred at the Wright State University Campus-Wide Celebration of Research, Scholarship and Creative Activities on April 8, 2011</p>