Accession Number:

AD1079680

Title:

Cocyclic Hadamard Matrices: An Efficient Search Based Algorithm

Descriptive Note:

[Technical Report, Doctoral Thesis]

Corporate Author:

AIR FORCE INSTITUTE OF TECHNOLOGY WRIGHT-PATTERSON AFB OH

Personal Author(s):

• Turner, Jonathan S.

Report Date:

2019-06-13

Pagination or Media Count:

124

Abstract:

This dissertation is 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 also presents an efficient sorting and comparison algorithm based upon symmetric functions and unique Legendre Pairs.

Descriptors:

• air force
• inverse problems
• united states government
• algorithms
• coding
• department of defense
• governments
• discrete fourier transforms
• heuristic methods
• decoding
• experimental design
• systems engineering
• united states
• applied mathematics
• combinatorial analysis
• counting methods
• cryptography
• digital signal processing
• equations
• error correction codes

Subject Categories:

• Numerical Mathematics

Distribution Statement:

[A, Approved For Public Release]