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The Characterization of 2n-Periodic Binary Sequences with Fixed 1-Error Linear Complexity

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Sequences and Their Applications – SETA 2006 (SETA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4086))

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Abstract

The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, using fast algorithms for computing the linear complexity and the k-error linear complexity of 2n-periodic binary sequences, Meidl determined the counting function and expected value for the 1-error linear complexity of 2n-periodic binary sequences. In this paper, we study the linear complexity and the 1-error linear complexity of 2n-periodic binary sequences. Some interesting properties of the linear complexity and the 1-error linear complexity of 2n-periodic binary sequences are obtained. Using these properties, we characterize the 2n-periodic binary sequences with fixed 1-error linear complexity. Along the way, we obtain a new approach to derive the counting function for the 1-error linear complexity of 2n-periodic binary sequences. Finally, we give new fast algorithms for computing the 1-error linear complexity and locating the error positions for 2n-periodic binary sequences.

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Author information

Authors and Affiliations

  1. Temasek Laboratories, National University of Singapore, 5 Sports Drive 2, Singapore, 117508, Republic of Singapore

    Fang-Wei Fu

  2. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

  3. Department of Mathematics, Nankai University, Tianjin, 300071, P.R. China

    Fang-Wei Fu & Ming Su

Authors
  1. Fang-Wei Fu
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  2. Harald Niederreiter
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  3. Ming Su
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Guang Gong

  2. Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

  3. Department of Electrical and Electronic Engineering, Yonsei University, 121-749, Seoul, Korea

    Hong-Yeop Song

  4. Dept. of Electronics and Electrical Engineering, Pohang University of Science and Technology (POSTECH), 790-784, Pohang, Kyungbuk, Korea

    Kyeongcheol Yang

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© 2006 Springer-Verlag Berlin Heidelberg

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Fu, FW., Niederreiter, H., Su, M. (2006). The Characterization of 2n-Periodic Binary Sequences with Fixed 1-Error Linear Complexity. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_8

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  • DOI: https://doi.org/10.1007/11863854_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44523-4

  • Online ISBN: 978-3-540-44524-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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