Legendre Pairs of Lengths ℓ ≡ 0 (Mod 5)

Authors

Ilias S. Kotsireas, Wilfrid Laurier University
Christopher Koutschan, Austrian Academy of Sciences
Dursun Bulutoglu, Air Force Institute of Technology
David M. Arquette, Air Force Institute of Technology
Jonathan S. Turner, Air Force Institute of Technology
Kenneth J. Ryan, West Virginia University

Document Type

Article

Publication Date

11-10-2023

Abstract

By assuming a type of balance for length ℓ = 87 and nontrivial subgroups of multiplier groups of Legendre pairs (LPs) for length ℓ = 85 , we find LPs of these lengths. We then study the power spectral density (PSD) values of m compressions of LPs of length 5 m . We also formulate a conjecture for LPs of lengths ℓ ≡ 0 (mod 5) and demonstrate how it can be used to decrease the search space and storage requirements for finding such LPs. The newly found LPs decrease the number of integers in the range ≤ 200 for which the existence question of LPs remains unsolved from 12 to 10.

Comments

© The Authors. This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Version note: This page pointed to the preprint version at arXiv.org. That version is still available at this link within the arXiv repository: 10.48550/arXiv.2111.02105

DOI

10.1515/spma-2023-0105

Source Publication

Special Matrices

Recommended Citation

Kotsireas, I. S., Koutschan, C., Bulutoglu, D. A., Arquette, D. M., Turner, J. S., & Ryan, K. J. (2023). Legendre pairs of lengths ℓ ≡ 0 (mod 5). Special Matrices, 11(1), 20230105. https://doi.org/10.1515/spma-2023-0105