The linear complexity of related prime sequences

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Green D. H. and Garcia–Perera L. P. 2004The linear complexity of related prime sequencesProc. R. Soc. Lond. A.460487–498http://doi.org/10.1098/rspa.2003.1216SectionRestricted accessThe linear complexity of related prime sequences D. H. Green D. H. Green Digital Communications Research Group, Department of Electrical Engineering and Electronics, UMIST, PO Box 88, Manchester M60 1QD, UK () Google Scholar Find this author on PubMed Search for more papers by this author and L. P. Garcia–Perera L. P. Garcia–Perera Digital Communications Research Group, Department of Electrical Engineering and Electronics, UMIST, PO Box 88, Manchester M60 1QD, UK () Google Scholar Find this author on PubMed Search for more papers by this author D. H. Green D. H. Green Digital Communications Research Group, Department of Electrical Engineering and Electronics, UMIST, PO Box 88, Manchester M60 1QD, UK () Google Scholar Find this author on PubMed Search for more papers by this author and L. P. Garcia–Perera L. P. Garcia–Perera Digital Communications Research Group, Department of Electrical Engineering and Electronics, UMIST, PO Box 88, Manchester M60 1QD, UK () Google Scholar Find this author on PubMed Search for more papers by this author Published:08 February 2004https://doi.org/10.1098/rspa.2003.1216AbstractPolyphase related–prime (RP) sequences can be constructed from the modified combination of two polyphase power–residue sequences and are generalizations of the two–phase modified Jacobi sequences, which include the twin–prime sequences as a special case. These sequences have also been referred to as cyclotomic sequences. RP sequences have been conjectured to possess high linear complexity under certain conditions and this is now confirmed theoretically for the q–phase case when q is a prime. The linear complexity of an RP sequence of length Λ= r . s, where r and s are distinct primes, is shown to depend on the relationship between the two primes used in the construction of the sequence and their selected primitive roots, and on the value assigned to the initial digit of the sequence. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Petersen T, Ceko M, Paganin D and Svalbe I (2022) A Curious Invariance Property of Certain Perfect Legendre Arrays: Stirring Without Mixing Discrete Geometry and Mathematical Morphology, 10.1007/978-3-031-19897-7_26, (330-340), . Edemskiy V and Antonova O (2011) About computation of the linear complexity of generalized cyclotomic sequences with period pq 2011 Fifth International Workshop on Signal Design and its Applications in Communications (IWSDA), 10.1109/IWSDA.2011.6159449, 978-1-61284-046-8, (9-12) Çeşmelioğlu A and Meidl W (2010) A General Approach to Construction and Determination of the Linear Complexity of Sequences Based on Cosets Sequences and Their Applications – SETA 2010, 10.1007/978-3-642-15874-2_10, (125-138), . Green D (2006) Linear complexity of modulo-m related prime sequences, IEE Proceedings - Computers and Digital Techniques, 10.1049/ip-cdt:20045120, 153:1, (31), . This Issue08 February 2004Volume 460Issue 2042 Article InformationDOI:https://doi.org/10.1098/rspa.2003.1216Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/02/2004Published in print08/02/2004 License: Citations and impact Keywordspower residuesPolyphase sequencesrelated Prime sequenceslinear complexitycyclotomic sequences