Some results for the existence of regular complex hadamard matrices

Abstract

In this paper, some infinite familes for the existence of regular complex Hadamard matrices of order 2v, for u ε S = S₁ ∪ S ₂ ∪ S₃ ∪ S₄, are given, where S ₁ = {p^2r:p ≡= 1 (mod 4) is a prime and r ≥ 0 is an integer}, S₂ = {2^2a3^2bN⁴:a, b = 0 or 1 and N is an integer}, S₃ = {5, 13, 17, 25, 37, 41, 61} ∪{p^2r:p ≡ 5 (mod 8) is a prime and r is a positive integer}, S₄ = {v₁ v₂. v₁ ε S₂ and v₂ ε S₃}. Moreover, when u ε S, we obtain a pair of regular and amicable complex Hadamard matrices of order 2v.