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Complex Weighing Matrices And Orthogonal Designs, Jennifer Seberry, Albert L. Whiteman
Complex Weighing Matrices And Orthogonal Designs, Jennifer Seberry, Albert L. Whiteman
Faculty of Informatics - Papers (Archive)
Galois fields G,F(q2) are used to obtain a new infinite family of complex weighing matrices. CW(q+l,q), q =1 (mod 8), and type P = [R – S S* - R*] where R and S are symmetric complex circulants. These matrices are used to construct orthogonal designs. Some unsolved cases of Geramita and Geramita are also settled.
Some Remarks On Amicable Orthogonal Designs, Jennifer Seberry
Some Remarks On Amicable Orthogonal Designs, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We present some new results on amicable orthogonal designs. We obtain amicable Hadamard matrices of order 24 .211 and a skew Hadamard matrix of order 24.295 which were previously not known.
All Directed Bibds With K = 3 Exist, Jennifer Seberry, David Skillicorn
All Directed Bibds With K = 3 Exist, Jennifer Seberry, David Skillicorn
Faculty of Informatics - Papers (Archive)
A directed BIBD with parameters (v,b,r,k,λ*) is a BIBD with parameters (v, b, r, k, 2λ*) in which each ordered pair of varieties occurs together in exactly λ* blocks. It is shown that λ*v(v - 1) = 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (v, b, r, k, λ*) BIBD with k = 3.
An Infinite Family Of Skew-Weighing Matrices, Jennifer Seberry
An Infinite Family Of Skew-Weighing Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We show that orthogonal designs of type (l,k) exist for all k = 0,1,...,2 .15-1, in order 2t .15, t ≥ 4 a positive integer. Hence there exist skew-symmetric weighing matrices W(2t .15,k) for all k = 0,1,... ,2t .15-1.
A Construction For Generalized Hadamard Matrices, Jennifer Seberry
A Construction For Generalized Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We prove that if pv and pr -1 are both prime powers then there is a generalized Hadamard matrix of order pr(pr -1) with elements from the elementary abelian group Zp x...x Zp. This result was motivated by results of Rajkundlia on BIBD's. This result is then used to produce pr -1 mutually orthogonal F-squares F(pr(pr -1); pr -1).
Some Infinite Classes Of Hadamard Matrices, Jennifer Seberry
Some Infinite Classes Of Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
A recursive method of A. C. Mukhopadhay is used to obtain several new infinite classes of Hadamard matrices. Unfortunately none of these constructions give previously unknown Hadamard matrices of order <40,000.
All Dbibds With Block Size Four Exist, Deborah J. Street, Jennifer Seberry
All Dbibds With Block Size Four Exist, Deborah J. Street, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
A directed balanced incomplete block design with parameters (v,b,r,k,λ*), is a balanced incomplete block design with parameters (v,b,r,k,2λ*), in which the blocks are regarded as ordered k-tuples and in which each ordered pair of elements occurs in λ* blocks. By generalizing results of Hanani, we show that the necessary conditions for the existence of these designs, when k = 4, are sufficient.
Higher Dimensional Orthogonal Designs And Hadamard Matrices, Jennifer Seberry
Higher Dimensional Orthogonal Designs And Hadamard Matrices, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We construct n-dimensional orthogonal designs of type (1, 1)n, side 2 and propriety (2,2,...,2). These are then used to show that orthogonal designs of type (2t, 2t)n, side 2t+1 and propriety (2,2,...,2) exist.