View Item 
      •   Home
      • 1. Schools
      • College of Science
      • School of Physical and Mathematical Sciences (SPMS)
      • SPMS Journal Articles
      • View Item
      •   Home
      • 1. Schools
      • College of Science
      • School of Physical and Mathematical Sciences (SPMS)
      • SPMS Journal Articles
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.
      Subject Lookup

      Browse

      All of DR-NTUCommunities & CollectionsTitlesAuthorsBy DateSubjectsThis CollectionTitlesAuthorsBy DateSubjects

      My Account

      Login

      Statistics

      Most Popular ItemsStatistics by CountryMost Popular Authors

      About DR-NTU

      On the algebraic structure of quasi-cyclic codes I : finite fields

      Thumbnail
      28. On the algebraic structure of quasi-cyclic codes I finite fields.pdf (387.3Kb)
      Author
      Ling, San
      Sole, Patrick
      Date of Issue
      2001
      School
      School of Physical and Mathematical Sciences
      Version
      Accepted version
      Abstract
      A new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the Chinese remainder theorem (CRT), or of the discrete Fourier transform (DFT), that ring can be decomposed into a direct product of fields. That ring decomposition in turn yields a code construction from codes of lower lengths which turns out to be in some cases the celebrated squaring and cubing constructions and in other cases the (u+υ|u-υ) and Vandermonde constructions. All binary extended quadratic residue codes of length a multiple of three are shown to be attainable by the cubing construction. Quinting and septing constructions are introduced. Other results made possible by the ring decomposition are a characterization of self-dual quasi-cyclic codes, and a trace representation that generalizes that of cyclic codes.
      Subject
      DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation
      Type
      Journal Article
      Series/Journal Title
      IEEE transactions on information theory
      Rights
      © 2001 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [DOI: http://dx.doi.org/10.1109/18.959257].
      Collections
      • SPMS Journal Articles
      http://dx.doi.org/10.1109/18.959257
      Get published version (via Digital Object Identifier)

      Show full item record


      NTU Library, Nanyang Avenue, Singapore 639798 © 2011 Nanyang Technological University. All rights reserved.
      DSpace software copyright © 2002-2015  DuraSpace
      Contact Us | Send Feedback
      Share |    
      Theme by 
      Atmire NV
       

       


      NTU Library, Nanyang Avenue, Singapore 639798 © 2011 Nanyang Technological University. All rights reserved.
      DSpace software copyright © 2002-2015  DuraSpace
      Contact Us | Send Feedback
      Share |    
      Theme by 
      Atmire NV
       

       

      DCSIMG