On FCSR Memory Sequences

  • Tian Tian
  • Wen-Feng Qi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4086)


In this paper we investigate FCSR memory sequences in two aspects, period and complementarity property. We show that an FCSR memory sequence shares the same period with its associated binary sequence for a special kind of connection integers. Especially, binary sequences generated by an FCSR with such connection integers contain most of the l-sequences. Furthermore, for an l-sequence \(\underline{a}\) with the minimum connection integer q and \(\underline{m}=(m_{0},m_{1},...)\) its memory sequence, we prove m i +m \(_{i+{\it T}/2}\)=w–1 for i≥0, where T = per\((\underline{a})\) and w is the Hamming weight of q+1.


Binary Sequence Stream Cipher Cyclotomic Polynomial Memory Sequence Integer Addition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tian Tian
    • 1
  • Wen-Feng Qi
    • 1
  1. 1.Department of Applied MathematicsZhengzhou Information Engineering UniversityZhengzhouP.R. China

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