A theory of Ternary complementary pairs

Craigen, R; Koukouvinos, C

dc.contributor.author	Craigen, R	en
dc.contributor.author	Koukouvinos, C	en
dc.date.accessioned	2014-03-01T01:16:04Z
dc.date.available	2014-03-01T01:16:04Z
dc.date.issued	2001	en
dc.identifier.issn	0097-3165	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13908
dc.subject	Binary Sequence	en
dc.subject	Signal Processing	en
dc.subject.classification	Mathematics	en
dc.subject.other	SEQUENCES	en
dc.title	A theory of Ternary complementary pairs	en
heal.type	journalArticle	en
heal.identifier.primary	10.1006/jcta.2001.3189	en
heal.identifier.secondary	http://dx.doi.org/10.1006/jcta.2001.3189	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	Sequences with zero autocorrelation are of interest because of their use in constructing orthogonal matrices and because of applications in signal processing, range finding devices, and spectroscopy, Golay sequences, which are pairs of binary sequences (i.e., all entries are +/-1) with zero autocorrelation, have been Studied extensively, yet are known only in lengths 2(a)10(b)26(c). Ternary complementary pairs are pairs of (0, +/-1)-sequences with zero autocorrelation (thus, Golay pairs are ternary complementary pairs with no 0's). Other kinds of pairs of sequences with zero autocorrelation, such as those admitting complex units for nonzero entries, are studied in similar contexts. Work on ternary complementary pairs is scattered throughout the combinatorics and engineering literature where the majority approach has been to classify pairs first by length and then by deficiency (the number of 0's in a pair); however, we adopt a more natural classification, first by weight (the number of nonzero entries) and then by length. We use this perspective to redevelop the basic theory of ternary complementary pairs, showing how to construct all known pairs from a handful of initial pairs we call primitive, We display all primitive pairs up to length 14, more than doubling the number that could be inferred from the existing literature. (C) 2001 Academic Press.	en
heal.publisher	ACADEMIC PRESS INC	en
heal.journalName	Journal of Combinatorial Theory. Series A	en
dc.identifier.doi	10.1006/jcta.2001.3189	en
dc.identifier.isi	ISI:000172162400008	en
dc.identifier.volume	96	en
dc.identifier.issue	2	en
dc.identifier.spage	358	en
dc.identifier.epage	375	en