Complete characterization of the first descent point distribution for the $k$error linear complexity of $2^n$periodic binary sequences
Pages: 429  444,
Issue 3,
August
2017
doi:10.3934/amc.2017036 Abstract
References
Full text (390.7K)
Related Articles
Jianqin Zhou  Department of Computing, Curtin University, Perth, WA 6102, Australia (email)
Wanquan Liu  Department of Computing, Curtin University of Technology, Perth, WA 6102, Australia (email)
Xifeng Wang  School of Computer Science, Anhui Univ. of Technology, Maanshan 243032, China (email)
1 
C. S. Ding, Lower bounds on the weight complexity of cascaded binary sequences, in Proc. Auscrypt'90 Adv. Crypt., SpringerVerlag, 1990, 3943. 

2 
C. S. Ding, G. Z. Xiao and W. J. Shan, The Stability Theory of Stream Ciphers, SpringerVerlag, Berlin, 1991, 8588. 

3 
T. Etzion, N. Kalouptsidis, N. Kolokotronis, K. Limniotis and K. G. Paterson, Properties of the error linear complexity spectrum, IEEE Trans. Inf. Theory, 55 (2009), 46814686. 

4 
F. Fu, H. Niederreiter and M. Su, The characterization of $2^n$periodic binary sequences with fixed 1error linear complexity, in SETA 2006 (eds. G. Gong et al), Springer, 2006, 88103. 

5 
R. A. Games and A. H. Chan, A fast algorithm for determining the complexity of a binary sequence with period $2^n$, IEEE Trans. Inf. Theory, 29 (1983), 144146. 

6 
Y. K. Han, J. H. Chung and K. Yang, On the $k$error linear complexity of $p^m$periodic binary sequences, IEEE Trans. Inf. Theory, 53 (2007), 22972304. 

7 
T. Kaida, S. Uehara and K. Imamura, An algorithm for the $k$error linear complexity of sequences over GF($p^m$) with period $p^n$, $p$ a prime, Inf. Comput., 151 (1999), 134147. 

8 
R. Kavuluru, Characterization of $2^n$periodic binary sequences with fixed 2error or 3error linear complexity, Des. Codes Crypt., 53 (2009), 7597. 

9 
N. Kolokotronis, P. Rizomiliotis and N. Kalouptsidis, Minimum linear span approximation of binary sequences, IEEE Trans. Inf. Theory, 48 (2002), 27582764. 

10 
K. Kurosawa, F. Sato, T. Sakata and W. Kishimoto, A relationship between linear complexity and $k$error linear complexity, IEEE Trans. Inf. Theory, 46 (2000), 694698. 

11 
A. Lauder and K. Paterson, Computing the error linear complexity spectrum of a binary sequence of period $2^n$, IEEE Trans. Inf. Theory, 49 (2003), 273280. 

12 
W. Meidl, How many bits have to be changed to decrease the linear complexity?, Des. Codes Crypt., 33 (2004), 109122. 

13 
W. Meidl, On the stablity of $2^n$periodic binary sequences, IEEE Trans. Inf. Theory, 51 (2005), 11511155. 

14 
F. Pi and W. F. Qi, The 4error linear complexity of $2^n$periodic binary sequences with linear complexity $2^n2^m2^l$, ACTA Electr. Sin. (in Chinese), 39 (2011), 29142920. 

15 
R. A. Rueppel, Analysis and Design of Stream Ciphers, SpringerVerlag, Berlin, 1986. 

16 
M. Stamp and C. F. Martin, An algorithm for the $k$error linear complexity of binary sequences with period $2^n$, IEEE Trans. Inf. Theory, 39 (1993), 13981401. 

17 
G. Z. Xiao, S. M. Wei, K. Y. Lam and K. Imamura, A fast algorithm for determining the linear complexity of a sequence with period $p^n$ over $GF(q)$, IEEE Trans. Inf. Theory, 46 (2000), 22032206. 

18 
J. Q. Zhou, On the $k$error linear complexity of sequences with period 2$p^n$ over GF(q), Des. Codes Crypt., 58 (2011), 279296. 

19 
J. Q. Zhou and W. Q. Liu, The $k$error linear complexity distribution for $2^n$periodic binary sequences, Des. Codes Crypt., 73 (2014), 5575. 

20 
J. Q. Zhou, J. Liu and W. Q. Liu, The 4error linear complexity distribution for $2^n$periodic binary sequences, 2013, preprint, arXiv:1310.0132 

21 
J. Q. Zhou, W. Q. Liu and G. L. Zhou, Cube theory and stable $k$error linear complexity for periodic sequences, in Inscrypt 2013, Springer, 7085. 

22 
F. X. Zhu and W. F. Qi, The 2error linear complexity of $2^n$periodic binary sequences with linear complexity $2^n$1, J. Electronics (China), 24 (2007), 390395. 

Go to top
