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Full-Text Articles in Physical Sciences and Mathematics
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.
On Circulant Best Matrices And Their Applications, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Circulant Best Matrices And Their Applications, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
Call four type 1(1,-1) matrices, x1,x2,x3,x4; of the same group of order m (odd) with the properties (i) (Xi-I)T = -(Xi-I), i=1,2,3, (ii)XT4 = X4 and the diagonal elements are positive, (iii) XiXj = XjXi and (iv) X1XT1 + X2XT2+X3XT3 +X4XT4 = 4mIm, best matrices. We use a computer to give, for the first time, all inequivalent best matrices of odd order m ≤31. Inequivalent best matrices of order m, m odd, can be used to find inequivalent skew-Hadamard matrices of order 4m. We use best matrices of order 1/4(s2+3) to construct new orthogonal designs, including new OD(2s2+6;1,1,2,2,s2,s2).
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 …
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We obtain explicit formulae for the values of the v j minors, j = 0, 1,2 of (1, -1) incidence matrices of SBIBD(v, k, λ). This allows us to obtain explicit information on the growth problem for families of matrices with moderate growth. An open problem remains to establish whether the (1, -1) CP incidence matrices of SBIBD(v, k, λ), can have growth greater than v for families other than Hadamard families.