Legendre G‐array pairs and the theoretical unification of several G‐array families
Abstract
We investigate how Legendre ‐array pairs are related to several different perfect binary ‐array families. In particular we study the relations between Legendre ‐array pairs, Sidelnikov‐Lempel‐Cohn‐Eastman ‐arrays, Yamada‐Pott ‐array pairs, Ding‐Helleseth‐Martinsen ‐arrays, Yamada ‐arrays, Szekeres ‐array pairs, Paley ‐array pairs, and Baumert ‐array pairs. Our work also solves one of the two open problems posed by Ding. Moreover, we provide several computer search‐based existence and nonexistence results regarding Legendre ‐array pairs. Finally, by using cyclotomic cosets, we provide a previously unknown Legendre ‐array pair.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 15, 2020
- Source ID
- 10.1002/jcd.21745
Entities
People
- D. A. Bulutoglu
- J. R. Hollon
- K. T. Arasu
Organizations
- Air Force Institute of Technology
- Air Force Office of Scientific Research