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On the amicability of orthogonal designs

✍ Scribed by W. H. Holzmann; H. Kharaghani

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
134 KB
Volume
17
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

Although it is known that the maximum number of variables in two amicable orthogonal designs of order 2^n^p, where p is an odd integer, never exceeds 2__n__+2, not much is known about the existence of amicable orthogonal designs lacking zero entries that have 2__n__+2 variables in total. In this paper we develop two methods to construct amicable orthogonal designs of order 2^n^p where p odd, with no zero entries and with the total number of variables equal or nearly equal to 2__n__+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. Β© 2009 Wiley Periodicals, Inc. J Combin Designs 17: 240‐252, 2009

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