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 ℤq−1-arrays, Yamada-Pott G-array pairs, Ding-Helleseth-Martinsen ℤ2×ℤmp-arrays, Yamada ℤ(q−1)/2-arrays, Szekeres ℤmp-array pairs, Paley ℤmp-array pairs, and Baumert ℤm1p1×ℤm2p2-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 ℤn-array pairs. Finally, by using cyclotomic cosets, we provide a previously unknown Legendre ℤ57-array pair.
Journal of Combinatorial Designs
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)