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#### Article: The linear complexity of whiteman's generalized cyclotomic sequences of period p {m+1}q n+1

Title The linear complexity of whiteman's generalized cyclotomic sequences of period p {m+1}q n+1 Hu, LYue, QWang, M Generalized Cyclotomic NumberLinear Complexity 2012 I E E E. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?puNumber=18 IEEE Transactions on Information Theory, 2012, v. 58 n. 8, p. 5534-5543 How to Cite? In this paper, we mainly get three results. First, let p, q be distinct primes with \gcd ((p-1)p,(q-1)q)=\gcd (p-1,q-1)=e ; we give a method to compute the linear complexity of Whiteman's generalized cyclotomic sequences of period p^{m+1}q n+1. Second, if e=4, we compute the exact linear complexity of Whiteman's generalized cyclotomic sequences. Third, if p \equiv q \equiv 5∼({\rm mod}∼8), \gcd (p-1, q-1)=4, and we fix a common primitive root g of both p and q, then 2\in H-{0}=(g), which is a subgroup of the multiplicative group Z-{pq} \ast, if and only if Whiteman's generalized cyclotomic numbers of order 4 depend on the decomposition pq=a^{2}+4b 2 with 4\vert b. © 1963-2012 IEEE. http://hdl.handle.net/10722/175531 0018-94482015 Impact Factor: 1.7372015 SCImago Journal Rankings: 1.433 WOS:000306518600036 References in Scopus

DC FieldValueLanguage
dc.contributor.authorHu, Len_US
dc.contributor.authorYue, Qen_US
dc.contributor.authorWang, Men_US
dc.date.accessioned2012-11-26T08:59:05Z-
dc.date.available2012-11-26T08:59:05Z-
dc.date.issued2012en_US
dc.identifier.citationIEEE Transactions on Information Theory, 2012, v. 58 n. 8, p. 5534-5543en_US
dc.identifier.issn0018-9448en_US
dc.identifier.urihttp://hdl.handle.net/10722/175531-
dc.description.abstractIn this paper, we mainly get three results. First, let p, q be distinct primes with \gcd ((p-1)p,(q-1)q)=\gcd (p-1,q-1)=e ; we give a method to compute the linear complexity of Whiteman's generalized cyclotomic sequences of period p^{m+1}q n+1. Second, if e=4, we compute the exact linear complexity of Whiteman's generalized cyclotomic sequences. Third, if p \equiv q \equiv 5∼({\rm mod}∼8), \gcd (p-1, q-1)=4, and we fix a common primitive root g of both p and q, then 2\in H-{0}=(g), which is a subgroup of the multiplicative group Z-{pq} \ast, if and only if Whiteman's generalized cyclotomic numbers of order 4 depend on the decomposition pq=a^{2}+4b 2 with 4\vert b. © 1963-2012 IEEE.en_US
dc.languageengen_US
dc.publisherI E E E. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?puNumber=18en_US
dc.relation.ispartofIEEE Transactions on Information Theoryen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectGeneralized Cyclotomic Numberen_US
dc.subjectLinear Complexityen_US
dc.titleThe linear complexity of whiteman's generalized cyclotomic sequences of period p {m+1}q n+1en_US
dc.typeArticleen_US
dc.identifier.emailWang, M: magwang@hku.hken_US
dc.identifier.authorityWang, M=rp00967en_US
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1109/TIT.2012.2196254en_US
dc.identifier.scopuseid_2-s2.0-84863936920en_US
dc.identifier.hkuros203256-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84863936920&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume58en_US
dc.identifier.issue8en_US
dc.identifier.spage5534en_US
dc.identifier.epage5543en_US
dc.identifier.isiWOS:000306518600036-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridHu, L=54949492300en_US
dc.identifier.scopusauthoridYue, Q=7005528517en_US
dc.identifier.scopusauthoridWang, M=8723779700en_US