• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.3
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• pp.609-616
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• 2014

Large linear span makes difficult to predict, so this study is important to the security and code system. It has been studied about the non-linear binary sequences having low correlation values and large linear span. In this paper we analyze the linear span of $S^r_a(t)=Tr^m_1\{[Tr^n_m(a{\alpha}^t+{\alpha}^{dt})]^r\}$ ($a{\in}GF(2^m)$, $0{\leq}t{\leq}2^m-2$) where n=2m and $d=2^{m-2}(2^m+3)$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.4
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• pp.730-736
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• 2012

PN(Pseudo Noise) sequences play an important role in wireless communications, such as in a CDMA(code division multiple access) communication system. If there is a crash when multiple users simultaneously connected to a system, then PN sequences with low correlation help to minimize multiple access interference in such communication system. In this paper we propose a family of non-linear extended binary sequences with low cross-correlations and the family include $m$-sequence, GMW sequence, Kasami sequence and No sequence with optimal cross-correlation in terms of Welch bound. And we analyze cross-correlation of these sequences.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.8
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• pp.1686-1692
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• 2012

Spreading sequence play an important role in wireless communications, such as in a CDMA(code division multiple access) communication system and multi-carrier spectrum communication system. Spreading sequences with low cross-correlation, in a direct-sequence spread spectrum communication system, help to minimize multiple access interference and to increase security degree of system. Analysis of cross-correlations between the sequences is a necessary process to design sequences. However it require lots of computing time for analysis of cross-correlations between sequences. In this paper we propose a method which is possible to compute effectively cross-correlation using subfield in the process of practical computation of cross-correlation between nonlinear binary sequences.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.7 no.4
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• pp.81-90
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• 1997

키 수열 발생기는 함수 조합 형태에 따라 여러 가지로 분류될 수 있으며, 비도 기본 요소(랜덤 특성, 주기, 선형 복잡도, 상관 면역도, 키 수열의 수 등)는 비선형 함수에 따라 달라진다. 모든 기본 요소를 잘 만족하는 키 수열 발생기는 설계가 어렵지만, 각 요소별로 특성이 뛰어난 발생기를 잘 조합하면 고비도 시스템을 설계할 수 있다. 본 논문에서는 선형 복잡도와 상관 면역도 측면에서 강한 개선된 합산 수열 발생기와 키 수열 수사 많은 일반화된 메모리 다수열 발생기를 조합하여 혼합형 수열 발생기를 제안하고, 비도 수준을 분석하였다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.3
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• pp.619-626
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• 2013

The design of PN(Pseudo Noise) sequences with good cross-correlation properties is important for many research areas in communication systems. In this paper we propose new family of binary sequences $S^r=\{Tr_1^m\{[Tr_m^n(a{\alpha}^t+{\alpha}^{dt})]^r\}{\mid}a{\in}GF(2^n),\;0{\leq}t<2^n-1\}$ composed of Gold-like sequences and find the value of cross-correlation function when $d=2^{n-1}(3{\cdot}2^m-1)$, where n=2k, gcd(r, $2^m-1$)=1. Also we analyze the linear span of $S^r$ for some special r. Proposed sequences are extension of Gold-like sequences and GMW-sequences.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2012.05a
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• pp.228-231
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• 2012

In this paper we propose a new family of nonlinear binary sequences generated by $m$-sequences for decimations $d=2^{k-1}(2^{s+1}-2^k+2^{k(i+1)}-2^{ki}-1)/(2^s-1)$ where $n=2k$, $i$ is odd and $s$ is such that $2s$ divides $k$. And we analyze the cross-correlation function between two $m$-sequences for new decimations $d$. Proposed sequences is extension of Rosendahl's sequnces and Dobbertin's sequences.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.12
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• pp.2875-2882
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• 2013

The design of PN(Pseudo Noise) sequences with good cross-correlation properties is important for many research areas in communication systems. Also analyses of cross-correlation frequency between designed sequences have been researched. In this paper we analyze of cross-correlation distribution and properties of non-linear binary sequences family $S^r=\{Tr^m_1\{[Tr^n_m(a{\alpha}^t+{\alpha}^{dt}]^r\}{\mid}a{\in}GF(2^m),0{\leq}t &lt; 2^n-1\}$, where $gcd(r,2^m-1)=1$ with 5-valued cross-correlation.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.4
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• pp.539-544
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• 2011

Balanced binary sequences of period $2^n-1(n{\geq}1)$ having the two-valued autocorrelation function have many applications in spread-spectrum communications system. In this paper we propose new nonlinear binary sequences which are constructed from Legendre sequences with the same cross-correlation as the sequences proposed by Cho. These sequences include the m-sequences, GMW sequences, Kasami sequences and No sequences which are described in terms of the trace function over a finite field. Also the proposed sequences have more low cross-correlation distribution than the quadratic form sequences proposed by Klapper.

• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.2
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• pp.263-269
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• 2012

Code-Division Multiple-Access(CDMA) allows several users simultaneous access to a common channel by assigning a distinct pseudonoise sequence called spectrum code to each user. Each user in a CDMA system uses a assigned spectrum code to modulate their signal. Choosing the codes used to modulate the signal is very important in the performance of CDMA systems. The best performance will occur when there is good separation between the signal of a desired user and the signals of other users. The receiver synchronizes the code to recover the data. The use of an independent code allows multiple users to access the same frequency band at the same time. In this paper we propose a generalized model of non-linear binary sequence using trace function and analyze cross-correlation of these sequences. These sequences with low correlation, large linear span and large family size, in a direct-sequence spread spectrum communication system, help to minimize multiple access interference, increase security degree of system and enlarge user number.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.3
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• pp.77-85
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• 2002

A Research of binary random sequence generator that uses a linear shift register had been studied since the 1970s. These generators were used in stream cipher. In general, the binary random sequence generator consists of linear shift registers that generate sequences of maximum period and a nonlinear filter function or a nonlinear combination function to generate a sequence of high linear complexity. Therefore, To generate a sequence that have long period as well as high linear complexity becomes an important factor to estimate safety of stream cipher. Usually, the maximum period of the sequence generated by a linear feedback shift register with L resistors is less than or equal to $2^L$-1. In this paper, we propose new binary random sequence generator that consist of L registers and 2 sub-characteristic polynomials. According to an initial state vector, the least period of the sequence generated by the proposed generator is equal to or ions than it of the sequence created by the general linear feedback shift register, and its linear complexity is increased too.