On the amicability of orthogonal designs |
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Authors: | W H Holzmann H Kharaghani |
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Institution: | Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4 |
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Abstract: | Although it is known that the maximum number of variables in two amicable orthogonal designs of order 2np, where p is an odd integer, never exceeds 2n+2, not much is known about the existence of amicable orthogonal designs lacking zero entries that have 2n+2 variables in total. In this paper we develop two methods to construct amicable orthogonal designs of order 2np where p odd, with no zero entries and with the total number of variables equal or nearly equal to 2n+2. In doing so, we make a surprising connection between the two concepts of amicable sets of matrices and an amicable pair of matrices. With the recent discovery of a link between the theory of amicable orthogonal designs and space‐time codes, this paper may have applications in space‐time codes. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 240‐252, 2009 |
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Keywords: | amicable orthogonal designs amicable set of matrices Goethals– Seidel array circulant matrices |
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