• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.5
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• pp.1138-1144
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• 2013

Cross-correlation functions of maximal period sequences have been studied for decades. In this paper, we find the cross-correlation values of non-linear sequences $S_a^r(t)=Tr_1^m\{[Tr_m^n(a{\alpha}^t+{\alpha}^{dt})]^r\}$ having the maximal period $2^n-1$ for Niho type decimation $d=2^{m-2}(2^m+3)$, where n=2m. In particular, we call d Niho type decimation in case $d{\equiv}1(mod\;2^m-1)$. And we analyze the cross-correlation distributions of $S_a^r(t)$ when the phase shift ${\tau}=(2^m+1)k(0{\leq}k{\leq}2^m-2)$ and provide experiment results.

• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.4
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• pp.821-826
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• 2012

p-ary sequences of period $N=2^k-1$ are widely used in many areas of engineering and sciences. Some well-known applications include coding theory, code-division multiple-access (CDMA) communications, and stream cipher systems. The analysis of cross-correlations of these sequences is a very important problem in p-ary sequences research. In this paper, we analyze cross-correlations of p-ary sequences which is associated with the equation $(x+1)^d=x^d+1$ over finite fields.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.903-911
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• 2012

Let $\{u(t)\}$ and $\{u(dt)\}$ be two maximal length sequences of period $2^n-1$. The cross-correlation is defined by $C_d({\tau})=\sum{_{t=0}^{2^n-2}}(-1)^{u(t+{\tau})+v(t)$ for ${\tau}=0,1,{\cdots},2^n-2$. In this paper, we propose a new proof for finding the values and the number of occurrences of each value of $C_d({\tau})$ when $d=2^{k-2}(2^k+3)$, where $n=2k$, $k$ is a positive integer.

• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.6
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• pp.1369-1375
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• 2012

One of important problems in the theory of sequences is to determine the values and number of occurrences of each value taken on by the cross-correlation. In this paper, we find the values and the number of occurrences of each value of cross-correlation between an m-sequence u(t) of period $2^n-1$ and its decimation $u(dt)(0{\leq}t{\leq}2^n-2)$ where n=2m, 2s|m and $d=(2^{2m}+2^{2s+1}-2^{m+s+1}-1)/(2^s-1)$. Also we show that a family of decimations leads to a four-valued cross-correlation.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.179-188
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• 2013

In this paper, we study the number of solutions to the equation $(x+1)^d=x^d+1$. This equation gives the value of the third power sum equation in case of Niho type exponents and is helpful in finding the distribution of the values $C_d({\tau})$. We provide the number of the solutions using the new method.