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A review and new symmetric conference matrices

Journal Article


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Abstract


  • The paper deals with symmetric conference matrices which were first highlighted by Vitold Belevitch, who showed that such matrices mapped to lossless telephone connections. The goal of this paper is developing a theory of conference matrices using the preliminary research results. Methods: Extreme (by determinant) solutions were obtained by minimization of the maximum of matrix elements absolute values, followed by their subsequent classification. Results: We give the known properties of symmetric conference matrices, known orders and illustrations for some elementary and some interesting cases. We restrict our attention in this note to symmetric conference matrices. We give two symmetric conference matrices of order 46 which are inequivalent to those given by Rudi Mathon and show they lead to two new families of symmetric conference matrices of order $5 \times 9^{2t+1} + 1$, t ≥ 0 is an integer. Practical relevance: Web addresses are given for other illustrations and other matrices with similar properties. Algorithms of building symmetric conference matrices have been used for developing research software.

Publication Date


  • 2014

Citation


  • Balonin, N. A.. & Seberry, J. (2014). A review and new symmetric conference matrices. Informatsionno-upravliaiushchie sistemy, 71 (4), 2-7.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3757&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2748

Number Of Pages


  • 5

Start Page


  • 2

End Page


  • 7

Volume


  • 71

Issue


  • 4

Place Of Publication


  • Russian Federation

Abstract


  • The paper deals with symmetric conference matrices which were first highlighted by Vitold Belevitch, who showed that such matrices mapped to lossless telephone connections. The goal of this paper is developing a theory of conference matrices using the preliminary research results. Methods: Extreme (by determinant) solutions were obtained by minimization of the maximum of matrix elements absolute values, followed by their subsequent classification. Results: We give the known properties of symmetric conference matrices, known orders and illustrations for some elementary and some interesting cases. We restrict our attention in this note to symmetric conference matrices. We give two symmetric conference matrices of order 46 which are inequivalent to those given by Rudi Mathon and show they lead to two new families of symmetric conference matrices of order $5 \times 9^{2t+1} + 1$, t ≥ 0 is an integer. Practical relevance: Web addresses are given for other illustrations and other matrices with similar properties. Algorithms of building symmetric conference matrices have been used for developing research software.

Publication Date


  • 2014

Citation


  • Balonin, N. A.. & Seberry, J. (2014). A review and new symmetric conference matrices. Informatsionno-upravliaiushchie sistemy, 71 (4), 2-7.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3757&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2748

Number Of Pages


  • 5

Start Page


  • 2

End Page


  • 7

Volume


  • 71

Issue


  • 4

Place Of Publication


  • Russian Federation