On symmetric incidence matrices of projective planes
Designs, Codes and Cryptography
Finite geometries
Eigenvalues of Finite Projective Planes with an Abelian Cartesian Group
Designs, Codes and Cryptography
A Concise Guide to Complex Hadamard Matrices
Open Systems & Information Dynamics
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The paper studies a generalized Hadamard matrix H= (g_{ij}) of order n with entries g_{ij}from a group G of order n. We assumethat H satisfies: (i)For m \neq k, G = \{g_{mi} g_{ki}^{-1}\midi = 1, \ldots , n\}; (ii) g_{1i} = g_{i1} = 1for each i; (iii) g_{ij}^{-1} = g_{ji}for all i, j. Conditions(i) and (ii) occur whenever G is a(P, L)-transitivityfor a projective plane of order n. Condition (iii)holds in the case that H affords a symmetric incidencematrix for the plane. The paper proves that G mustbe a 2-group and extends previous work to the case that nis a square.