Orthogonal Arrays and Legendre Pairs

Abstract

Well-designed experiments greatly improve test and evaluation. Efficient experiments reduce the cost and time of running tests while improving the quality of the information obtained. Orthogonal Arrays (OAs) and Hadamard matrices are used as designed experiments to glean as much information as possible about a process with limited resources. However, constructing OAs and Hadamard matrices in general is a very difficult problem. Finding Legendre pairs (LPs) results in the construction of Hadamard matrices. This research studies the classification problem of OAs and the existence problem of LPs. In doing so, it makes two contributions to the discipline. First, it improves upon previous classification results of 2-symbol OAs of even-strength t and t 2 columns. Second, it presents previously unknown impossible values for the dimension of the convex hull of all feasible points to the LP problem improving our understanding of its feasible set.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 22, 2022
Accession Number
AD1181178

Entities

People

  • Kristopher N. Kilpatrick

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Classification
  • Combinatorial Analysis
  • Construction
  • Data Science
  • Department Of Defense
  • Engineering
  • Experimental Design
  • Factorial Design
  • Governments
  • Information Science
  • Integer Programming
  • Mathematics
  • Standards
  • Statistics
  • Test And Evaluation
  • Theses
  • United States
  • United States Government
  • Vector Spaces

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Calculus or Mathematical Analysis
  • Traumatic Brain Injury (TBI) and Cognitive Aging in the Guam and Border Populations Affected by Alzheimer's Disease and Tau-Associated Dementias.