`a`
Advances in Mathematics of Communications (AMC)
 

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., Springer-Verlag, 1990, 39-43.       
2 C. S. Ding, G. Z. Xiao and W. J. Shan, The Stability Theory of Stream Ciphers, Springer-Verlag, Berlin, 1991, 85-88.       
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), 4681-4686.       
4 F. Fu, H. Niederreiter and M. Su, The characterization of $2^n$-periodic binary sequences with fixed 1-error linear complexity, in SETA 2006 (eds. G. Gong et al), Springer, 2006, 88-103.       
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), 144-146.       
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), 2297-2304.       
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), 134-147.       
8 R. Kavuluru, Characterization of $2^n$-periodic binary sequences with fixed 2-error or 3-error linear complexity, Des. Codes Crypt., 53 (2009), 75-97.       
9 N. Kolokotronis, P. Rizomiliotis and N. Kalouptsidis, Minimum linear span approximation of binary sequences, IEEE Trans. Inf. Theory, 48 (2002), 2758-2764.       
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), 694-698.       
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), 273-280.       
12 W. Meidl, How many bits have to be changed to decrease the linear complexity?, Des. Codes Crypt., 33 (2004), 109-122.       
13 W. Meidl, On the stablity of $2^n$-periodic binary sequences, IEEE Trans. Inf. Theory, 51 (2005), 1151-1155.       
14 F. Pi and W. F. Qi, The 4-error linear complexity of $2^n$-periodic binary sequences with linear complexity $2^n-2^m-2^l$, ACTA Electr. Sin. (in Chinese), 39 (2011), 2914-2920.
15 R. A. Rueppel, Analysis and Design of Stream Ciphers, Springer-Verlag, 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), 1398-1401.       
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), 2203-2206.       
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), 279-296.       
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), 55-75.       
20 J. Q. Zhou, J. Liu and W. Q. Liu, The 4-error 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, 70-85.       
22 F. X. Zhu and W. F. Qi, The 2-error linear complexity of $2^n$-periodic binary sequences with linear complexity $2^n$-1, J. Electronics (China), 24 (2007), 390-395.       

Go to top