Date of Award
6-16-2019
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Department of Mathematics and Statistics
First Advisor
Andrew J. Geyer, PhD
Abstract
This dissertation serves as the culmination of three papers. “Counting the decimation classes of binary vectors with relatively prime fixed-density" presents the first non-exhaustive decimation class counting algorithm. “A Novel Approach to Relatively Prime Fixed Density Bracelet Generation in Constant Amortized Time" presents a novel lexicon for binary vectors based upon the Discrete Fourier Transform, and develops a bracelet generation method based upon the same. “A Novel Legendre Pair Generation Algorithm" expands upon the bracelet generation algorithm and includes additional constraints imposed by Legendre Pairs. It further presents an efficient sorting and comparison algorithm based upon symmetric functions, as well as multiple unique Legendre Pairs.
AFIT Designator
AFIT-ENC-DS-19-J-074
DTIC Accession Number
AD1079680
Recommended Citation
Turner, Jonathan S., "Cocyclic Hadamard Matrices: An Efficient Search Based Algorithm" (2019). Theses and Dissertations. 2191.
https://scholar.afit.edu/etd/2191