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Full-Text Articles in Physical Sciences and Mathematics
On Orthogonal Designs In Order 48, W. H. Holzmann, H Kharaghani, Jennifer Seberry, B. Tayfeh-Rezaie
On Orthogonal Designs In Order 48, W. H. Holzmann, H Kharaghani, Jennifer Seberry, B. Tayfeh-Rezaie
Faculty of Informatics - Papers (Archive)
We show that all 3164 possible OD(48; s1, s2,s3) exist. In addition to the use of some classical techniques we employ two new method of construction.
Generalized Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Generalized Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Orthogonal designs and their special cases such as weighing matrices and Hadamard matrices have many applications in combinatorics, statistics, and coding theory as well as in signal processing. In this paper we generalize the definition of orthogonal designs, we give many constructions for these designs and we prove some multiplication theorems that, most of them, can also be applied in the special case of orthogonal designs. Some necessary conditions for the existence of generalized orthogonal designs are also given.
Necessary And Sufficient Conditions For Three And Four Variable Orthogonal Designs In Order 36, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Necessary And Sufficient Conditions For Three And Four Variable Orthogonal Designs In Order 36, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We use a new algorithm to find new sets of sequences with entries from {0, ±a, ±b, ±c, ±d}, on the commuting variables a, b, c, d, with zero autocorrelation function. Then we use these sequences to construct a series of new three and four variable orthogonal designs in order 36. We show that the necessary conditions plus (.s1, s2, s3, s4) not equal to 12816 18 816 221313 26721 36 816 4889 12825 191313 23 424 289 9 381015 8899 14425 22 916 are sufficient for the existence of an OD(36; s1, s2 s3, s4) constructed using four circulant …
A New Algorithm For Computer Searches For Orthogonal Designs, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
A New Algorithm For Computer Searches For Orthogonal Designs, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We present a new algorithm for computer searches for orthogonal designs. Then we use this algorithm to find new sets of sequences with entries from {0, ±a, ±b, ±c, ±d} on the commuting variables a, b, c, d with zero autocorrelation function.
Necessary And Sufficient Conditions For Two Variable Orthogonal Designs In Order 44: Addendum, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Necessary And Sufficient Conditions For Two Variable Orthogonal Designs In Order 44: Addendum, S. Georgiou, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
In our recent paper Necessary and sufficient conditions for some two variable orthogonal designs in order 44, Koukouvinos, Mitrouli and Seberry leave 7 cases unresolved. Using a new algorithm given in our paper A new algorithm for computer searches for orthogonal designs by the present four authors we are able to finally resolve all these cases. This note records that the necessary conditions for the existence of two variable designs constructed using four circulant matrices are sufficient. In particular of 484 potential cases 404 cases have been found, 68 cases do not exist and 12 cases cannot be constructed using …
New Orthogonal Designs And Sequences With Two And Three Variables In Order 28, C. Koukouvinos, Jennifer Seberry
New Orthogonal Designs And Sequences With Two And Three Variables In Order 28, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We give new sets of sequences with entries from {0, ±a, ±b, ±c} on the commuting variables a, b, c and zero autocorrelation function. Then we use these sequences to construct some new orthogonal de-signs. We show the necessary conditions for the existence of an OD(28; s1, s2, s3) plus the condition that (s1, s2, s3) ≠ (1,5,20) are sufficient conditions for the existence of an OD(28; s1, s2, s3). We also show the necessary conditions for the existence of an OD(28; s1, s2, s3) constructed using four circulant matrices are sufficient conditions for the existence of 4 — NPAF(s1, …
When The Necessary Conditions Are Not Sufficient: Sequences With Zero Autocorrelation Function, J. Horton, Jennifer Seberry
When The Necessary Conditions Are Not Sufficient: Sequences With Zero Autocorrelation Function, J. Horton, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Recently K. T. Arasu (personal communication) and Yoseph Strassler, in his PhD thesis, The Classification of Circulant Weighing Matrices of Weight 9, Bar-Ilan University, Ramat-Gan, 1997, have intensively studied circulant weighing matrices, or single sequences, with weight 9. They show many cases are non-existent. Here we give details of a search for two sequences with zero periodic autocorrelation and types (1,9), (1,16) and (4,9). We find some new cases but also many cases where the known necessary conditions are not sufficient. We instance a number of occasions when the known necessary conditions are not sufficient for the existence of weighing …
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
Faculty of Informatics - Papers (Archive)
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 …
Necessary And Sufficient Conditions For Some Two Variable Orthogonal Designs In Order 44, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Necessary And Sufficient Conditions For Some Two Variable Orthogonal Designs In Order 44, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We give a new algorithm which allows us to construct new sets of sequences with entries from the commuting variables 0, ± a, ± b, ± c, ± d with zero autocorrelation function. We show that for twelve cases if the designs exist they cannot be constracted using four circulant matrices in the Goethals-Seidel array. Further we show that the necessary conditions for the existence of an OD(44; s1, s2) are sufficient except possibly for the following 7 cases: (7, 32) (8, 31), (9, 30) (9, 33) (11,30) (13, 29) (15, 26) which could not be found because of the …