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On a special case of a conjecture of Ryser about Hadamard circulant matrices. (English) Zbl 1321.15052

Summary: There is no Hadamard circulant matrices \(H\) of order \(n>4\) with (a) first column \([x_1,\dots,x_n]^\ast\) where \(x_1(x_i +x_{\frac{n}{2}+i})>2\) for all \(i=1,\dots,n/2\) and (b) 2 such that \(A+B\) is symmetric, where \(A,B\) are matrices of order \(n/2\) such that the first \(n/2\) lines of \(H\) have the form \([A,B]\).

MSC:

15B34 Boolean and Hadamard matrices
11B30 Arithmetic combinatorics; higher degree uniformity
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