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Inequivalence Of Nega-Cyclic ±1 Matrices, R. Ang, Jennifer Seberry, Tadeusz A. Wysocki
Inequivalence Of Nega-Cyclic ±1 Matrices, R. Ang, Jennifer Seberry, Tadeusz A. Wysocki
Professor Jennifer Seberry
We study nega-cyclic ±1 matrices. We obtain preliminary results which are then used to decrease the search space. We find that there are 2, 4, 9, 23, 63, and 187 ip-equivalence classes for lengths 3, 5, 7, 9, 11, and 13 respectively. The matrices we find are used in a variant given here of the Goethals-Seidel array to form Hadamard matrices, the aim being to later check them for suitability for CDMA schemes.
New Weighing Matrices And Orthogonal Designs Constructed Using Two Sequences With Zero Autocorrelation Function - A Review, C. Koukouvinos, Jennifer Seberry
New Weighing Matrices And Orthogonal Designs Constructed Using Two Sequences With Zero Autocorrelation Function - A Review, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
The book, Orthogonal Designs: Quadratic Forms and Hadamard Matrices, Marcel Dekker, New York-Basel, 1979, by A. V. Geramita and Jennifer Seberry, has now been out of print for almost two decades. Many of the results on weighing matrices presented therein have been greatly improved. Here we review the theory, restate some results which are no longer available and expand on the existence of many new weighing matrices and orthogonal designs of order 2n where n is odd. We give a number of new constructions for orthogonal designs. Then using number theory, linear algebra and computer searches we find new weighing …