Further explorations into ternary complementary pairs

Craigen, R; Georgiou, S; Gibson, W; Koukouvinos, C

dc.contributor.author	Craigen, R	en
dc.contributor.author	Georgiou, S	en
dc.contributor.author	Gibson, W	en
dc.contributor.author	Koukouvinos, C	en
dc.date.accessioned	2014-03-01T01:24:26Z
dc.date.available	2014-03-01T01:24:26Z
dc.date.issued	2006	en
dc.identifier.issn	0097-3165	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17265
dc.subject	Primitive pairs	en
dc.subject	Ternary complementary pairs	en
dc.subject	Zero autocorrelation sequences	en
dc.subject.classification	Mathematics	en
dc.subject.other	SEQUENCES	en
dc.title	Further explorations into ternary complementary pairs	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jcta.2005.07.013	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jcta.2005.07.013	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	In [R. Craigen, C. Koukouvinos, A theory of ternary complementary pairs, J. Combin. Theory Ser. A 96 (2001) 358-375], we proposed a systematic approach to the theory of ternary complementary pairs (TCPs) and showed how all pairs known then could be constructed using a single elementary product, the natural equivalence relations, and a handful of pairs which we called primitive. We also introduced more new primitive pairs than could be inferred previously, concluding with some conjectures reflecting the patterns that were beginning to arise in light of the new approach. In this paper we take what appears to be the natural next step, by investigating these patterns among those lengths and weights that are within easy computational distance from the last length considered therein, length 14. We give complete results up to length 21, and partial results up to length 28. (Ironically, although we proceed analytically by weight first then length, for computational reasons we are bound, in this empirical investigation, to proceed according to length first.) Thus we provide support for the previous conjectures, and shed enough new light to speculate further as to the likely ultimate shape of the theory. Since short term work on TCPs will require massive acquisition of data about small pairs, we also discuss affixes-a computational strategy that arose out of the investigations culminating in this article. (c) 2006 Elsevier Inc. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	Journal of Combinatorial Theory. Series A	en
dc.identifier.doi	10.1016/j.jcta.2005.07.013	en
dc.identifier.isi	ISI:000239537400003	en
dc.identifier.volume	113	en
dc.identifier.issue	6	en
dc.identifier.spage	952	en
dc.identifier.epage	965	en