New constructions of Hadamard matrices

  title={New constructions of Hadamard matrices},
  author={K. H. Leung and K. Momihara},
  journal={J. Comb. Theory, Ser. A},
In this paper, we obtain a number of new infinite families of Hadamard matrices. Our constructions are based on four new constructions of difference families with four or eight blocks. By applying the Wallis-Whiteman array or the Kharaghani array to the difference families constructed, we obtain new Hadamard matrices of order $4(uv+1)$ for $u=2$ and $v\in \Phi_1\cup \Phi_2 \cup \Phi_3 \cup \Phi_4$; and for $u\in \{3,5\}$ and $v\in \Phi_1\cup \Phi_2 \cup \Phi_3$. Here, $\Phi_1=\{q^2:q\equiv 1… Expand
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