New weighing matrices and orthogonal designs constructed using two sequences with zero autocorrelation function - A review

Koukouvinos, C; Seberry, J

dc.contributor.author	Koukouvinos, C	en
dc.contributor.author	Seberry, J	en
dc.date.accessioned	2014-03-01T01:14:52Z
dc.date.available	2014-03-01T01:14:52Z
dc.date.issued	1999	en
dc.identifier.issn	0378-3758	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13258
dc.subject	62K10	en
dc.subject	Algorithm	en
dc.subject	Autocorrelation	en
dc.subject	Construction	en
dc.subject	Orthogonal design	en
dc.subject	Primary 05B20	en
dc.subject	Secondary 62K05	en
dc.subject	Sequences	en
dc.subject	Weighing matrices	en
dc.subject.classification	Statistics & Probability	en
dc.title	New weighing matrices and orthogonal designs constructed using two sequences with zero autocorrelation function - A review	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0378-3758(99)00006-3	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0378-3758(99)00006-3	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	The book, Orthogonal Designs: Quadratic Forms and Hadamard Matrices, Marcel Dekker, New York-Baser, 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 matrices and orthogonal designs. We have reviewed completely the weighing matrix conjecture for orders 2n, n less than or equal to 35, n odd. The previously known results for weighing matrices for n less than or equal to 21 are summarized here, and new results given, leaving three unresolved cases. The results for weighing matrices for n greater than or equal to 23 are presented here for the first time. For orders n, 23 less than or equal to n less than or equal to 25, 3 remain unsolved as do a further 106 cases for orders 27 less than or equal to n less than or equal to 49. We also review completely the orthogonal design conjecture for two variables in orders equivalent to 2 (mod4). The results for orders 2n, n odd, 15 less than or equal to n less than or equal to 33 being given here for the first time. (C) 1999 Elsevier Science B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Journal of Statistical Planning and Inference	en
dc.identifier.doi	10.1016/S0378-3758(99)00006-3	en
dc.identifier.isi	ISI:000082471900011	en
dc.identifier.volume	81	en
dc.identifier.issue	1	en
dc.identifier.spage	153	en
dc.identifier.epage	182	en