## Cube theory and k-error linear complexity profile

dc.contributor.author | Zhou, J. | |

dc.contributor.author | Liu, Wan-Quan | |

dc.contributor.author | Wang, X. | |

dc.date.accessioned | 2017-01-30T15:26:01Z | |

dc.date.available | 2017-01-30T15:26:01Z | |

dc.date.created | 2016-09-11T19:30:38Z | |

dc.date.issued | 2016 | |

dc.identifier.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. | |

dc.identifier.uri | http://hdl.handle.net/20.500.11937/46243 | |

dc.identifier.doi | 10.14257/ijsia.2016.10.7.15 | |

dc.description.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. | |

dc.title | Cube theory and k-error linear complexity profile | |

dc.type | Journal Article | |

dcterms.source.volume | 10 | |

dcterms.source.number | 7 | |

dcterms.source.startPage | 169 | |

dcterms.source.endPage | 184 | |

dcterms.source.issn | 1738-9976 | |

dcterms.source.title | International Journal of Security and its Applications | |

curtin.department | Department of Computing | |

curtin.accessStatus | Open access via publisher |

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