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On Circulant Complex Hadamard Matrices |
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| Authors: | K. T. Arasu Warwick de Launey S. L. Ma |
| Affiliation: | (1) Department of Mathematics and Statistics, Wright State University, Dayton, OH, 45435;(2) Center for Communication Research, 4320 Westerra Court, San Diego, CA, 92121;(3) Department of Mathematics, National University of Singapore, Kent Ridge, Singapore, 119260, Republic of Singapore |
| Abstract: | We show that a circulant complex Hadamard matrix of order n is equivalent to a relative difference set in the group C4×Cn where the forbidden subgroup is the unique subgroup of order two which is contained in the C4 component. We obtain non-existence results for these relative difference sets. Our results are sufficient to prove there are no circulant complex Hadamard matrices for many orders. |
| Keywords: | relative difference set complex Hadamard matrix circulant matrix |
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