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Legendre G-Array Pairs And The Theoretical Unification Of Several G-Array Families, K. T. Arasu, Dursun A. Bulutoglu, J. R. Hollon

Faculty Publications

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. …