K.T. Arasu (Advisor), Yuqing Chen (Committee Member), Jason Deibel (Committee Member), Xiaoyu Liu (Committee Member)
Doctor of Philosophy (PhD)
Binary sequences and arrays, their higher dimensional counterparts, play a critical role in today's technologically advanced world. This thesis explores such sequences and their optimality under various conditions along with their applicability to problems in engineering such as communication and radar systems. A new asymptotically orthogonal type of matrix is defined with computational examples given along with infinite theoretical families. A high energy ternary sequence is developed and shown to have real world promise by simulation of its radar ambiguity function and frame synchronization. Proposed within is an extended and more complete definition for Doppler tolerance by which sequences may be compared for use in radar. A method for turning existing families of binary optimal sequences in to ternary optimal sequences is given along with three example families by Sidelnikov-Lempel-Cohn-Eastman, Ding-Helleseth-Martinsen, and Paley. Various families of Legendre pairs are examined and special type, called a Yamada-Pott pair, is defined and explored giving interesting insight into various families of sequences. Finally, the optimality of binary sequences is discussed with searches for sequences with minimal sum-of-square autocorrelation gives rise to an order 39 matrix with large determinant, related to the D-Optimal design problem, and an affirmation of an optimal length 41 sequence.
Department or Program
Department of Mathematics and Statistics
Year Degree Awarded
Copyright 2018, all rights reserved. My ETD will be available under the "Fair Use" terms of copyright law.