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二元周期序列的k错误线性复杂度 被引量：5

On the k-Error Linear Complexity of Binary Period Sequences
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摘要 随着k的增大 ,序列k错误线性复杂度的值会从线性复杂度递减到 0 .对于周期为 2的方幂的二元序列 ,Kurosawa讨论了线性复杂度和k错误线性复杂度的关系 ,给出了使得序列的k错误线性复杂度严格小于序列的线性复杂度最小的k值 .本文利用多项式的权重关系给出了使得序列k错误线性复杂度再次减小的最小k值 . With the increase of k, the k-error linear complexity will decrease to 0 from the value of the linear complexity of the sequences. For the binary sequences whose period is a power of 2, a relationship between the linear complexity and k-error linear complexity is discussed by Kurosawa, which indicates the least value of the positive integer k such that the k-error linear complexity less than linear complexity. In this paper, using the Hamming weight of polynomials, the least k is given such that the k-error linear complexity decreased again.
作者 赵耀东 戚文峰
机构地区 郑州信息工程大学信息工程学院应用数学系
出处 《电子学报》 EI CAS CSCD 北大核心 2005年第1期12-16,共5页 Acta Electronica Sinica
基金 全国优秀博士学位论文专项基金 (No .2 0 0 0 60 ) 国家自然科学基金 (No.60 3730 92 )
关键词 序列密码 线性复杂度 k错误线性复杂度 Binary sequences Computational complexity Polynomials Theorem proving
分类号 TN918.1 [电子电信—通信与信息系统]
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参考文献8

  • 1K Kurosawa, F Sato, T Sakata, W Kishimoto. A relationship between linear complexity and k-error linear complexity [J]. IEEE IT -46:694-698.
  • 2James L Massey D J. Costello, J Justesen. Polynomial Weights and Code Constructions[J]. IEEE Trans IT. 1973, IT-19:101 - 110.
  • 3Mark Stamp, Clyde F Martin. An Algorithm for the k-error Linear Complexity of Binary Sequences with Period 2n[J]. IEEE Trans IT.July, 1993. IT - 39:1398 - 1401.
  • 4C Ding, O Xiao, W Shah. The slability theory of stream ciphers[M]. In Springer Verlag, lecture Notes in Computer Science, 1991.561.
  • 5W Meidl, H Niederreiter. Counting Functions and Expected Values for the k-error Linear Complexity[J]. Finite Fields and Their Applications 8.2002.142 - 154.
  • 6W Meidl, H Niederreiter. Linear Complexity, k-error Linear Complexity, and the Discrete Fourier Transform [J]. Journal of Complexity. 2002,18.87 - 103.
  • 7R A Rueppel. Linear Complexity and Random Sequences [A].Advances in Cryptology-EUROCRYPT' 85 [C]. Lecture Notes in Computer Science, Vol. 219, Berlin, Springer Verlag, 1986. 167 -188.
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同被引文献18

  • 1Zhu Fengxiang Qi Wenfeng.THE 2-ERROR LINEAR COMPLEXITY OF 2~n-PERIODIC BINARY SEQUENCES WITH LINEAR COMPLEXITY 2~n-1[J].Journal of Electronics(China),2007,24(3):390-395. 被引量：21
  • 2Ding Cunsheng, Xiao Guozhen, Shan Weijuan. The Stability Theory of Stream Ciphers[M]. Berlin, Germany: Springer-Verlag, 1991.
  • 3Stamp M, Martin C F. An Algorithm for the K-error Linear Complexity of Binary Sequences with Period 2n[J]. IEEE Trans. on Inform. Theory, 1993, 39(4): 1398-1401.
  • 4Kurosawa K, Sato F, Sakata T, et al. A Relationship Between Linear Complexity and K-error Linear Complexity[J]. IEEE Trans. on Inform. Theory, 2000, 46(2): 694-698.
  • 5Meidl W. On the Stability of 2n-periodic Binary Sequences[J]. IEEE Trans. on Inform. Theory, 2005, 51(3): 1151-1155.
  • 6E R Berlekamp.Algebraic coding theory[M].New York:McGraw-Mill,1986.
  • 7R Games,A Chan.A fast algorithm for determining the complexity of a binary sequence with period 2n[J].IEEE Trans Inform Theory,1983,29 (1):144-146.
  • 8J L Massey,D Costello,J Justesen.Polynomial weights and code constructions[J].IEEE Trans Inform Theory,1973,19(1):101 -110.
  • 9K Kurosawa,F Sato,T Sakata,W Kishmoto.A relation between linear complexity and k-error linear complexity[J].IEEE Trans Inform Theory,2000,46 (2):694-698.
  • 10张禾瑞．近世代数基础[M]．北京：高等教育出版社，1978.94-95．

引证文献5

二级引证文献8

电子学报
2005年 第1期

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