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Some Notes on the Linear Complexity of Sidel'nikov-Lempel-Cohn-Eastman Sequences
2006
Designs, Codes and Cryptography
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We continue the study of the linear complexity of binary sequences, independently introduced by Sidel'nikov and Lempel, Cohn, and Eastman. ...
Moreover, we prove a general lower bound on the linear complexity profile for all of these sequences. ...
Acknowledgments The first author was supported by DSTA research grant R-394-000-011-422. The second author was supported by the Austrian Academy of Sciences and by the FWF research grant S8313. ...
doi:10.1007/s10623-005-6340-2
fatcat:f5j6oqh5fjaqtkmwalxj2sxyje
On a Theorem of Kyureghyan and Pott
[article]
2018
arXiv
pre-print
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Kyureghyan and Alexander Pott (Designs, Codes and Cryptography, 29, 149-164, 2003), the linear feedback polynomials of the Sidel'nikov-Lempel-Cohn-Eastman sequences were determined for some special cases ...
In this note, we give some counterexamples of Corollary 4 and Theorem 2 of that paper. ...
Pott determined the linear complexity and the linear feedback polynomials of the Sidel'nikov-Lempel-Cohn-Eastman sequences for some special cases. ...
arXiv:1810.02599v1
fatcat:7qwwxdc3dfdcpgt7nkorqpwbou
Multiplicities of Character Values of Binary Sidel'nikov-Lempel-Cohn-Eastman Sequences
[article]
2017
arXiv
pre-print
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Binary Sidel'nikov-Lempel-Cohn-Eastman sequences (or SLCE sequences) over F 2 have even period and almost perfect autocorrelation. ...
However, the evaluation of the linear complexity of these sequences is really difficult. In this paper, we continue the study of [1]. ...
Then the d-ary SLCE sequence s = (s 0 , s 1 , s 2 , · · · ) over F d can be defined by s n = i if α n + 1 ∈ C i for some i 0 otherwise SLCE sequences were introduced by Sidel'nikov [21] and Lempel, Cohn ...
arXiv:1702.05867v1
fatcat:zd2x2cf4mnbo3mhwjrpz3sjfhi
On the linear complexity of Legendre–Sidelnikov sequences
2013
Designs, Codes and Cryptography
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Then the Sidel'nikov (Lempel-Cohn-Eastman) sequence is defined: s n = 1, if η(g n + 1) = −1, 0, otherwise, n = 0, 1, . . . . ...
Then the Sidel'nikov (Lempel-Cohn-Eastman) sequence is defined: s n = 1, if η(g n + 1) = −1, 0, otherwise, n = 0, 1, . . . . ...
Result on the Linear Complexity-Theorem 1 Theorem 1 The linear complexity of Legendre-Sidelnikov sequences L(S) satisfies:
Experiments
Result on the Linear Complexity-Theorem 2 Theorem 2 Let q = 2r ...
doi:10.1007/s10623-013-9889-1
fatcat:g2cvsghzu5bs7nyctw3lbnktgu
Derivation of autocorrelation distributions of Sidel'nikov sequences using cyclotomic numbers
2005
Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.
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The frequency of each autocorrelation value of an M -ary Sidel'nikov sequence is expressed in terms of the cyclotomic numbers of order M . ...
In this paper, we derived the autocorrelation distributions, i.e., the values and the number of occurrences of each value of the autocorrelation function of Sidel'nikov sequences. ...
Later, Lempel, Cohn, and Eastman [4] independently introduced the binary Sidel'nikov sequences of period p n − 1. ...
doi:10.1109/isit.2005.1523687
dblp:conf/isit/KimCNC05
fatcat:7t4xkrigvjdqdmj5jarkqdjvla
Linear Complexity over F p of Ternary Sidel'nikov Sequences
[chapter]
2006
Lecture Notes in Computer Science
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As a special case, the linear complexity of the ternary Sidel'nikov sequence is presented. ...
It turns out that the linear complexity of a ternary Sidel'nikov sequence with the symbol k0 = 1 at the (p m − 1)/2-th position is nearly close to the period of the sequence, while that with k0 = 1 shows ...
This research was supported by the MIC, Korea, under the ITRC support program and by the MOE, the MOCIE, and the MOLAB, Korea, through the fostering project of the Laboratory of Excellency. ...
doi:10.1007/11863854_6
fatcat:7bifqs53cvbrrm2msd3oja6dc4
On the linear complexity of Sidel'nikov sequences over nonprime fields
2008
Journal of Complexity
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We show that several classes of Sidel'nikov sequences over arbitrary finite fields exhibit a large linear complexity. ...
For Sidel'nikov sequences over F 8 we provide exact values for their linear complexity. ...
Independently in [16] Lempel, Cohn and Eastman studied the sequence (1) for d = 2. In the following we suggest a natural generalization of the sequence (1) for arbitrary finite fields. ...
doi:10.1016/j.jco.2008.04.002
fatcat:q7xcodv73na7xorqnyipm5bkym
On the linear complexity of Sidel'nikov Sequences over F d
unpublished
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We study the linear complexity of sequences over the prime field F d introduced by Sidel'nikov. For several classes of period length we can show that these sequences have a large linear complexity. ...
Moreover, we prove a general lower bound on the linear complexity profile for all of these sequences. The obtained results extend known results on the binary case. ...
We will indicate how we can use this results to obtain more information on the linear complexity of the Sidel'nikov-Lempel-Cohn-Eastman Sequence. ...
fatcat:tdkfsk2wtjehhjhps7htgcdk7m