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    Cube theory and k-error linear complexity profile

    Access Status
    Open access via publisher
    Authors
    Zhou, J.
    Liu, Wan-Quan
    Wang, X.
    Date
    2016
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Zhou, J. and Liu, W. and Wang, X. 2016. Cube theory and k-error linear complexity profile. International Journal of Security and its Applications. 10 (7): pp. 169-184.
    Source Title
    International Journal of Security and its Applications
    DOI
    10.14257/ijsia.2016.10.7.15
    ISSN
    1738-9976
    School
    Department of Computing
    URI
    http://hdl.handle.net/20.500.11937/46243
    Collection
    • Curtin Research Publications
    Abstract

    © 2016 SERSC. The linear complexity and k-error linear complexity of a sequence have been used as important measures for keystream strength. In order to study k-error linear complexity of binary sequences with period 2n, a new tool called cube theory is developed. In this paper, we first give a general decomposition approach to decompose a binary sequence with period 2n into some disjoint cubes. Second, a counting formula for m-cubes with the same linear complexity is derived, which is equivalent to the counting formula for k-error vectors. The counting formula of 2n-periodic binary sequences which can be decomposed into more than one cube is also investigated, which extends an important result by Etzion et al.. Finally, we study 2n-periodic binary sequences with the given k-error linear complexity profile. Consequently, the complete counting formula of 2n-periodic binary sequences with given k-error linear complexity profile of descent points 2, 4 and 6 is derived. The periodic sequences having the prescribed k-error linear complexity profile with descent points 1, 3, 5 and 7 are also briefly discussed.

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