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wright1307537681.pdf (360.55 KB)
ETD Abstract Container
Abstract Header
Multilevel Hadamard Matrices
Author Info
Parker, Keli Siqueiros
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=wright1307537681
Abstract Details
Year and Degree
2011, Master of Science (MS), Wright State University, Mathematics.
Abstract
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 HH
T
= wI for orders 3 and 4, and give new constructions for other orders of MHMs.
Committee
K. T. Arasu, PhD (Committee Chair)
Yuqing Chen, PhD (Committee Member)
Xiaoyu Liu, PhD (Committee Member)
Pages
56 p.
Subject Headings
Mathematics
Keywords
Hadamard Matrix
;
multilevel Hadamard matrix
;
weighing matrix
;
circulant matrices
;
zero correlation zone sequence
;
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Citations
Parker, K. S. (2011).
Multilevel Hadamard Matrices
[Master's thesis, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1307537681
APA Style (7th edition)
Parker, Keli.
Multilevel Hadamard Matrices.
2011. Wright State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=wright1307537681.
MLA Style (8th edition)
Parker, Keli. "Multilevel Hadamard Matrices." Master's thesis, Wright State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=wright1307537681
Chicago Manual of Style (17th edition)
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Document number:
wright1307537681
Download Count:
666
Copyright Info
© 2011, all rights reserved.
This open access ETD is published by Wright State University and OhioLINK.