• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.10
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• pp.2181-2187
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• 2011

In this paper, a family of binary sequences generated by GMW sequences and No sequences is introduced and analyzed. Each sequence within a family has period $N=2^n-1$, n=2m and there are $2^m$ sequences within that family. We obtain auto and cross-correlation values and linear span of the synthesized sequence.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.11C
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• pp.1059-1065
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• 2007

In this paper, we propose a class of polyphase signature sequences, whose general odd correlation properties are useful for M-ary phase signaling systems. The maximum magnitude of the general odd correlation functions of the proposed sequences are investigated and compared with those of FZC (Frank-Zadoff-Chu) sequences and those of EOE (equivalent odd and even correlation) sequences. The performance of the asynchronous M-ary phase signaling systems using the proposed sequences is simulated and compared with that using FZC sequences in direct sequence code division multiple access (DS/CDMA) systems. The performance of the system using the proposed sequence is shown to be better than that using FZC sequences when the multipath fading is in existence.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.1C
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• pp.6-11
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• 2008

From a periodic sequence, we can obtain new sequences with a longer period by r-symbol insertion to each period. In this paper we review previous results on the linear complexity of periodic sequences obtained by r-symbol insertion. We derive the distribution of the linear complexity of 1-symbol insertion sequences obtained from m-sequences over GF(p), and prove some relationship between their linear complexity and the insertion position. Then, we analyze the k-error linear complexity of the 1-symbol insertion sequences from binary m-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.

• 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.

• 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 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.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.1
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• pp.13-19
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• 2011

Games gave the calculation method for the crosscorrelation function of a Kasami sequence and a No sequence that have been generated by the same primitive polynomial. In this paper, we calculate the crosscorrelation function of a Kasami sequence and a No sequence that have been generated by the same primitive polynomial with the periodic crosscorrelation function of two base sequences. Our method is different from the Games's method.

• 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.

• 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.