New constructions of Hadamard matrices
Abstract
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∈ 1 2 3 4; and for u∈ \3,5\ and v∈ 1 2 3. Here, 1=\q2:q 14 is a prime power\, 2=\n4∈ N:n 12\ \9n4∈ N:n 12\, 3=\5\ and 4=\13,37\. Moreover, our construction also yields new Hadamard matrices of order 8(uv+1) for any u∈ 1 2 and v∈ 1 2 3.
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