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

Document Type


Publication Date



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 ×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 Zn-array pairs. Finally, by using cyclotomic cosets, we provide a previously unknown Legendre Z57-array pair.