Legendre G-array Pairs and the Theoretical Unification of Several G-array Families

Authors

K. T. Arasu, Riverside Research
Dursun A. Bulutoglu, Air Force Institute of TechnologyFollow
J. R. Hollon, Applied Optimization, Inc.

Document Type

Article

Publication Date

2020

Abstract

We investigate how Legendre G-array pairs are related to several different perfect binary G-array families. In particular we study the relations between Legendre G-array pairs, Sidelnikov-Lempel-Cohn-Eastman ℤ_q−1-arrays, Yamada-Pott G-array pairs, Ding-Helleseth-Martinsen ℤ₂×ℤ^m_p-arrays, Yamada ℤ_(q−1)/2-arrays, Szekeres ℤ^m_p-array pairs, Paley ℤ^m_p-array pairs, and Baumert ℤ^m1_p1×ℤ^m2_p2-array pairs. Our work also solves one of the two open problems posed in Ding~[J. Combin. Des. 16 (2008), 164-171]. Moreover, we provide several computer search based existence and non-existence results regarding Legendre ℤ_n-array pairs. Finally, by using cyclotomic cosets, we provide a previously unknown Legendre ℤ₅₇-array pair.

Comments

This is the pre-peer reviewed version of the article as cited below, which has been published in final form at https://doi.org/10.1002/jcd.21745. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

Sourced from arXiv:2004.05608

DOI

10.1002/jcd.21745

Source Publication

Journal of Combinatorial Designs

Recommended Citation

Arasu, KT, Bulutoglu, DA, Hollon, JR. Legendre G ‐array pairs and the theoretical unification of several G ‐array families. J Combin Des. 2020; 1– 28. https://doi.org/10.1002/jcd.21745 (Published in advance of inclusion in issue)