k-error linear complexity of q-ary sequence of period p2

被引：0
|
作者：
Wu C. [1 ,2 ]
Xu C. [1 ]
Du X. [3 ]
机构：
[1] School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu
[2] Provincial Key Laboratory of Applied Mathematics, Putian University, Putian
[3] College of Mathematics and Statistics, Northwest Normal University, Lanzhou
来源：
Tongxin Xuebao/Journal on Communications | 2019年 / 40卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Fermat quotient sequence; Generic cyclotomic generator; k-error linear complexity; q-ary sequence; Stream cipher;
D O I：
10.11959/j.issn.1000-436x.2019230
中图分类号：
学科分类号：
摘要：
Based on element statistics in a matrix, a new efficient computing method for computing the k-error linear complexity of q-ary sequence of period p2 was proposed, where p,q were odd primes and q modulo p2 was primitive. A general result and a concrete proof were showed. To verify the correctness of the result, two kinds of q-ary sequence of period p2 were illustrated. Because the new method does not need iterative calculation and when it is implemented by program and compared with existing algorithms, the results show that the proposed new algorithm is significantly more efficient in calculating k-error linear complexity of q-ary sequence of period p2. © 2019, Editorial Board of Journal on Communications. All right reserved.
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页码：21 / 28
页数：7
相关论文
共 23 条
  • [1] Ruppel R., Analysis and Design of Stream Ciphers, (1986)
  • [2] Cusick T., Ding C., Renvall A., Stream Ciphers and Number Theory, (1998)
  • [3] Stamp M., Martin C., An algorithm for the k-error linear complexity of binary sequences with period 2<sup>n</sup> , IEEE Transactions on Information Theory, 39, 4, pp. 1389-1401, (1993)
  • [4] Ding C., Lower bounds on the weight complexity of cascaded binary sequences, International Conference on Cryptology, Lecture Notes in Computer Science, 453, pp. 39-43, (1991)
  • [5] Ding C., Xiao G., Shan W., The Stability Theory of Stream Ciphers, (1991)
  • [6] Golomb S., Gong G., Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar, (2005)
  • [7] Berlekamp E., Algebraic Coding Theory, (1968)
  • [8] Massey J., Shift register synthesis and BCH decoding, IEEE Transactions on Information Theory, 15, 1, pp. 122-127, (1969)
  • [9] Games R., Chan A., A fast algorithm for determining the complexity of a binary sequence with period 2<sup>n</sup> , IEEE Transactions on Information Theory, 29, 1, pp. 144-146, (1983)
  • [10] Meidl W., On the stability of 2<sup>n</sup>-periodic binary sequences, IEEE Transactions on Information Theory, 51, 3, pp. 1151-1155, (2005)
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