New orthogonal designs and sequences with two and three variables in order 28

Koukouvinos, C; Seberry, J

dc.contributor.author	Koukouvinos, C	en
dc.contributor.author	Seberry, J	en
dc.date.accessioned	2014-03-01T01:50:04Z
dc.date.available	2014-03-01T01:50:04Z
dc.date.issued	2000	en
dc.identifier.issn	0381-7032	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/25985
dc.subject	autocorrelation	en
dc.subject	construction	en
dc.subject	sequence	en
dc.subject	orthogonal design	en
dc.subject.classification	Mathematics	en
dc.title	New orthogonal designs and sequences with two and three variables in order 28	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2000	en
heal.abstract	We give new sets of sequences with zero autocorrelation function and entries from the set {0, +/-a, +/-b, +/-c} where a, b and c are commuting variables (which may also be set zero). Then we use these sequences to construct some new orthogonal designs. We show the known necessary conditions for the existence of an OD(28; s(1), s(2), s(3)) plus the condition that (s(1), s(2), s(3)) not equal (1, 5, 20) are sufficient conditions for the existence of an OD(28; s(1), s(2), s(3)). We also show the known necessary conditions for the existence of an OD(28; s(1), s(2), s(3)) constructed using four circulant matrices are sufficient conditions for the existence of 4-NPAF(s(1), s(2), s(3)) of length n for all lengths n greater than or equal to 7. We establish asymptotic existence results for OD(4N; s(1), s(2)) for 3 less than or equal to s(1) + S-2 less than or equal to 28. This leaves no cases undecided for 1 less than or equal to s(1) + s(2) less than or equal to 28 We show the known necessary conditions for the existence of an OD(28; s(1), s(2)) with 25 less than or equal to s(1) + s(2) less than or equal to 28, constructed using four circulant matrices, plus the condition that (S-1, s(2)) not equal (1, 26), (2, 25), (7, 19), (8, 19) or (13, 14), are sufficient conditions for the existence of 4-NPAF(s(1), s(2)) of length n for all lengths n greater than or equal to 7.	en
heal.publisher	CHARLES BABBAGE RES CTR	en
heal.journalName	ARS COMBINATORIA	en
dc.identifier.isi	ISI:000085703600007	en
dc.identifier.volume	54	en
dc.identifier.spage	97	en
dc.identifier.epage	108	en