2016/02/23 by Ebrahim Ghaderpour, Ghaderpour, Ebrahim
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Transport Systems and Technology #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.1602.07794
To appear in International Journal of Combinatorics (Hindawi). in Int. J. Combin. (Feb 2016)
arxiv created 2016/02/23 · openalex publication_date 2016/02/23 · arxiv updated 2016/02/26 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
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 weighing matrix 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.