Cyclic Difference Sets And Cyclic Hadamard Matrices

Details Cyclic Difference Sets And Cyclic Hadamard Matrices Cyclic Difference Sets And Cyclic Hadamard Matrices

2011-09-29

arxiv.org/abs/1110.1322v6

Mathematics

Number Theory

Simpler And Improved Version, 8 Pages

Scientific paper

The collection of cyclic Hadamard matrices {H = (a_{i - j}) : 0 <= i, j < n, and a_i = -1, 1} of order n 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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