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

DTIC pending

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