• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.6C
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• pp.582-588
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• 2006

In this paper, the relationship among M-ary Sidel'nikov sequences generated by different primitive elements and decimation are studied. Their autocorrelation function and autocorrelation distribution are derived. It is proved that Sidel'nikov sequences for a given period are equivalent under the decimation, cyclic shift, and scalar multiplication of the sequence.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.8C
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• pp.735-741
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• 2005

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. The frequency of each autocorrelation value of an M-ary Sidel'nikov sequence is expressed in terms of the cyclotomic numbers of order M. It is also pointed out that the total number of distinct autocorrelation values is dependent not oかy on M but also on the sequence, but always less than or equal to ($\frac{M}{2}$)+1.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1150-1156
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• 2006

In this paper we derive some lower bounds on the linear complexity and upper bounds on the 1-error linear complexity over $F_p$ of M-ary Sidel'nikov sequences of period $p^m-1$ when $M\geq3$ and $p\equiv{\pm}1$ mod M. In particular, we exactly compute the 1-error linear complexity of ternary Sidel'nikov sequences when $p^m-1$ and $m\geq4$. Based on these bounds we present the asymptotic behavior of the normalized linear complexity and the normalized 1-error linear complexity with respect to the period.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.10C
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• pp.929-934
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• 2007

In this paper, we enumerate the number of distinct autocorrelation distributions that M-ary Sidel'nikov sequences can have, while we change the primitive element for generating the sequence. Let p be a prime and $M|p^n-1$. For M=2, there is a unique autocorrelation disuibution. If M>2 and $M|p^k+1$ for some k, $1{\leq}k, then the autocorrelatin distribution of M-ary Sidel'nikov sequences is unique. If M>2 and $M{\nmid}p^k+1$ for any k, $1{\leq}k, then the autocorrelation distribution of M-ary Sidel'nikov sequences is less than or equal to ${\phi}(M)/k'(or\;{\phi}(M)/2k')$, where k' is the smallest integer satisfying $M|p^{k'}-1$.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.10C
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• pp.959-964
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• 2007

In this paper, for a positive integer M and a prime p such that $M|p^n-1$, families of M-ary sequences using the M-ary Sidel'nikov sequences with period $p^n-1$ are constructed. The family has its maximum magnitude of correlation values upper bounded by $3\sqrt{p^{n}}+6$ and the family size is $(M-1)^2(2^{n-1}-1)$+M-1 for p=2 or $(M-1)^2(p^n-3)/2+M(M-1)/2$ for an odd prime p.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.11
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• pp.1566-1573
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• 2021

Rendezvous is a process that assists nodes in a Cognitive Radio Networks (CRNs) to discover each other. In CRNs where a common control channel is unknown and a number of channels are given, it is important how two nodes find each other in a known search region. In this paper, I have proposed and analyzed a channel hopping sequence using Sidel'nikov sequence by which each node visits an available number of channels. I analyze the expected time to-rendezvous (TTR) mathematically. I also verify the Rendezvous performance of proposed sequence in the view of TTR under 2 user environment compared with JS algorithm and GOS algorithm. The Rendezvous performance of proposed sequence is much better than GOS algorithm and similar with JS algorithm. But when M is much smaller than p, the performance of proposed sequence is better than JS algorithm.