International Journal of Combinatorics
http://www.i-scholar.in/index.php/Ijco
International Journal of Combinatorics is a peer-reviewed, open access journal that publishes original research articles as well as review articles in all areas of combinatorics.en-USijcom@hindawi.com (Dr. Nantel Bergeron)ijcom@hindawi.com (Dr. Nantel Bergeron)Thu, 28 Apr 2016 11:29:58 +0000OJS 2.4.2.0http://blogs.law.harvard.edu/tech/rss60Some Nonexistence and Asymptotic Existence Results for Weighing Matrices
http://www.i-scholar.in/index.php/Ijco/article/view/98319
Orthogonal designs and weighing matrices have many applications in areas such as coding theory, cryptography, wireless networking, and communication. In this paper, we first show that if positive integer k cannot be written as the sum of three integer squares, then there does not exist any skew-symmetric weighingmatrix of order 4n and weight k, where n is an odd positive integer. Then we show that, for any square k, there is an integer N(k) such that, for each n ≥ N(k), there is a symmetric weighing matrix of order n and weight k. Moreover, we improve some of the asymptotic existence results for weighing matrices obtained by Eades, Geramita, and Seberry.Ebrahim Ghaderpourhttp://www.i-scholar.in/index.php/Ijco/article/view/98319