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http://dx.doi.org/10.14317/jami.2013.869

ANALYSIS OF THE SEQUENCES WITH OPTIMAL CROSS-CORRELATION PROPERTY  

Kwon, Min-Jeong (Department of Applied Mathematics, Pukyong National University)
Cho, Sung-Jin (Department of Applied Mathematics, Pukyong National University)
Publication Information
Journal of applied mathematics & informatics / v.31, no.5_6, 2013 , pp. 869-876 More about this Journal
Abstract
The design of large family size with the optimal cross-correlation property is important in spread spectrum and code division multiple access communication systems. In this paper we present the sequences with the decimation $d=2{\cdot}2^m-1$, calculate the cross-correlation spectrum for $0{\leq}t{\leq}2^n-2$ and count the number of the value $2^m-1$ occurring for $0{\leq}{\tau}2^n-2$. The sequences have the optimal cross-correlation property. The work on this paper can make it easier to count the number of the whole value occurring for $0{\leq}{\tau}2^n-2$.
Keywords
Finite field; decimation; cross-correlation functions; number of the occurrence;
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  • Reference
1 E.S. Selmer, Linear Recurrence Relations over Finite Fields, University of Bergen, 1966.
2 M. Simon, J. Omura, R. Scholtz, B. Levitt, Spread Spectrum Communications, Computer Science Press, 1985.
3 L.R. Welch, Lower bounds on the maximum cross-correlation of signals, IEEE Transac-tions on Information Theory, 20 (1974), 397-399.   DOI
4 N. Zierler, Linear recurring sequences, Journal of the Society for Industrial and Applied Mathematics, 7 (1976), 31-48.
5 R. Gold, Optimal binary sequences for spread spectrum multiplexing, IEEE Transactions on Information Theory, 13 (1967), 619-621.   DOI   ScienceOn
6 R. Gold, Maximal recursive sequences with 3-valued recursive cross-correlation functions, IEEE Transactions on Information Theory, 14 (1968), 154-156.   DOI
7 H.D. Kim, S.J. Cho, A New Proof about the decimation with Niho type fice-valued cross-correlation functions, J. Appl. Math. and Inform. 30 (2012), 903-911.
8 T. Helleseth, Some results about the cross-correlation function between two maximal linear sequences, Discrete Mathematics, 16 (1976), 209-232.   DOI   ScienceOn
9 T. Helleseth, J. Lahtonen, and P. Rosendahl,On certain equations over finite fields and cross-correlations of m-sequences, Coding, Cryptography and Combinatorics, Progress in Computer Science and Applied Logic, 23 (1984), 169-176.
10 T. Helleseth, A note on the cross-correlation function between two binary maximal length linear sequences, Discrete Mathematics, 23 (1978), 301-307.   DOI   ScienceOn
11 T. Kasami, Weight distribution of Bose-Chaudhuri-Hocquenghem codes, Combinatorial Mathematics and Its Applications, Chapel Hill, N.C., University of North Carolina Press, 1969.
12 R. Lidl and H. Niederreiter, Finite fields, Cambridge University Press, 1997.
13 R.J. McEliece, Correlation properties of sets of sequences derived from irreducible cyclic codes, Information and Control, 45 (1980), 18-25.   DOI   ScienceOn
14 Y. Niho, Multi-valued cross-correlation functions between two maximal linear recursive sequences, Ph.D thesis, University of Southern California, 1972.
15 D.V. Sarwate, M.B. Purseley, Crosscorrelation properties of pseudorandom and related sequences, Proceedings of the IEEE, 68 (1980), 593-619.   DOI   ScienceOn
16 R.A. Scholtz and L.R.Welch, GMW sequences, IEEE Transactions on Information Theory, 30 (1984), 548-553.   DOI
17 S.W. Golomb, Shift register sequences, Holden Day, 1967.