Mathematics – Number Theory
Scientific paper
2005-06-02
Mathematics
Number Theory
The old version uses analytical methods, this version uses algebraic methods, 7 pages
Scientific paper
The collection of cyclic Hadamard matrices {H=(a_{i-j}) : 0 \leq i,j < n, and ai = -1,1} of order n \geq 1 is characterized by the orthogonality relation HH^T = nI. Only two of such matrices are currently known. It will be shown that this collection consists of precisely two matrices. An application of this result implies that there are exactly seven Barker sequences over the binary set {-1,1}.
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