Browse > Article
http://dx.doi.org/10.13067/JKIECS.2011.6.4.539

Design of Binary Sequences with Optimal Cross-correlation Values  

Choi, Un-Sook (동명대학교 자율전공학부)
Cho, Sung-Jin (부경대학교 응용수학과)
Publication Information
The Journal of the Korea institute of electronic communication sciences / v.6, no.4, 2011 , pp. 539-544 More about this Journal
Abstract
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.
Keywords
cross-correlation; auto-correlation; trace; binary sequences; Legendre sequences; pseudorandom sequence;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 G. Gong, "New designs for signal sets with low cross correlation, balance property, and large linear span: GF(p) case," IEEE Trans. Inform. Theory, Vol. 4, pp. 2847-2867, 2002.
2 S.W. Golomb, "On the classification of balanced binary sequences of period $2^{n}-1$," IEEE trans. Inform. Theory, Vol. IT-26, No.6, pp. 730-732, 1980.
3 M.K. Simon, J.K. Omura, R.A. Scholtz, and B.K. Levitt, Spread Spectrum Communications, Vol. 1, Rockville, MD: Computer Science Press, 1985.
4 S.W. Golomb, "Shift Register Sequences," Holden Day, 1967.
5 R.A. Scholtz and R. Welch, "GMW sequences," IEEE Trans. Inform. Theory, Vol. IT-30, pp. 548-553, 1984.
6 J.S. No, H.K. Lee, H. Chuang, H.Y. Song, and K. Yang, "Trace representation of Legendre Sequences of Mersenne prime period," IEEE Trans. Inform. Theory, Vol. 42, No. 6, pp. 2254-2255, 1996.   DOI   ScienceOn
7 J.S. No, and P.V. Kumar, "A new family of binary pseudorandom sequences having optimal periodic correlation properties and large linear span," IEEE Trans. Inform. Theory, Vol. IT-35, No. 2, pp. 371-379, 1989.
8 T. Kasami, "Weight distribution of Bose- Chaudhuri-Hocquenghem codes," in Combinatorial Mathematics and Its Applications. Chapel Hill, NC: Univ. North Carolina Press, 1969.
9 A. Klapper, "Large Families of Sequences with Near-Optimal Correlations and Large Linear Span," IEEE Trans. Inform. Theory, Vol. 42, No. 4, pp. 1241-1248, 1996.   DOI   ScienceOn
10 U.S. Choi, S.J. Cho, H.D. Kim, "Attack using Phase Shifts of Shrunken Sequence", J. The Korea Institute of Electronic Communication Sciences, Vol. 6, No. 1, pp. 97-104, 2011.
11 J.G. Kim, S.J. Cho, U.S. Choi, Y.H. Hwang, " Crosscorrelation of Kasami sequences and No sequences", J. The Korea Institute of Electronic Communication Sciences, Vol. 6, No. 1, pp. 13-19, 2011.
12 U.S. Choi, S.J. Cho, J.G. Kim, " Analysis of Shrunken Sequences using LFSR and CA on $GF(2^{P})$", J. The Korea Institute of Electronic Communication Sciences, Vol. 5, No. 4, pp. 418-424, 2010.
13 S.J. Cho, U.S. Choi, H.D. Kim, H.J. An, " Analysis of nonlinear sequences based on shrinking generator", J. The Korea Institute of Electronic Communication Sciences, Vol. 5, No. 4, pp. 412-417, 2011.
14 S.J. Cho, S.H. Kwon, "A new family binary sequences with low correlation," (submitted).
15 L.R. Welch, "Lower bounds on the maximum cross-correlation of signals," IEEE Trans. Inform. Theory, Vol. IT-20, pp. 397-399, 1974.
16 R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press 1997.
17 J.S. No, "p-ary unified sequences : p-ary extended d-form sequences with ideal autocorrelation property," IEEE Trans. Inform. Theory, Vol. 48, No. 9, pp. 2540-2546, 2002.   DOI   ScienceOn
18 T. Helleseth and P.V. Kumar, "Sequences with low correlation," in Handbook of Coding Theory, V.S. Pless and W.C. Huffman, Eds., Amsterdam, The Vetherland: North-Holland, Vol. II, pp. 1765-1853, 1998.