The Journal of the Korea institute of electronic communication sciences (한국전자통신학회논문지)

Korea Institute of Electronic Communication Science (한국전자통신학회)
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Analysis of Cross-Correlation of m-sequences and Equation on Finite Fields

유한체상의 방정식과 m-수열의 상호상관관계 분석

  • Received : 2012.07.03
  • Accepted : 2012.08.09
  • Published : 2012.08.31
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Abstract

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.

주기가 $p^n-1$인 p진 수열은 부호이론, CDMA와 같은 통신시스템과 암호체계 등 많은 분야에서 폭넓게 응용되고 있다. 이러한 수열에 대한 상호상관관계에 대한 분석은 p진 수열의 연구에 있어 매우 중요한 문제이다. 본 논문에서는 유한체 위에서의 방정식 $(x+1)^d=x^d+1$의 해와 관련지어 p진 수열의 상호상관관계를 분석한다.

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References

  1. S.W. Golomb, "Shift Register Sequences," Holden Day, 1967.
  2. R.A. Scholtz and R. Welch, "GMW sequences," IEEE Trans. Inform. Theory, Vol. IT-30, pp. 548-553, 1984.
  3. 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. https://doi.org/10.1109/18.556617
  4. 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.
  5. T. Kasami, "Weight distribution of Bose-Chaudhuri-Hocquenghem codes," in Combinatorial Mathematics and Its Applications. Chapel Hill, NC: Univ. North Carolina Press, 1969.
  6. 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. https://doi.org/10.1109/18.508849
  7. S.J. Cho, Finite Fields with Their Applications, Kyowoosa Press, 2007.
  8. 조성진, 최언숙, 김한두, 안현주, "수축생성기에 기반한 비선형 수열의 분석", 한국전자통신학회 논문지, 5권, 4호, pp. 412-417, 2010.
  9. 김진경, 조성진, 최언숙, 황윤희, "Kasami 수열들과 No 수열들의 상호상관관계", 한국전자통신학회논문지, 6권, 1호, pp. 13-19, 2011.
  10. 최언숙, 조성진, "최적의 상호상관관계를 갖는 이진 수열의 설계", 한국전자통신학회논문지, 6권, 4호, pp. 539-544, 2011.
  11. 최언숙, 조성진, 권숙희, "확장된 비선형 이진수열의 상호상관관계 분석", 한국전자통신학회논문지, 7권, 2호, pp. 263-270, 2012.
  12. R. Gold, "Maximal recursive sequences with 3-valued cross-correlation functions," IEEE Trans. Inform. Theory, Vol. 14, pp. 154-156, 1967. https://doi.org/10.1109/TCT.1967.1082686
  13. T. Helleseth, J. Lahtonen and P. Rosendahl, "On Niho type cross-correlation functions of m-sequences," Finite Fields and Their Applications, Vol. 13, No. 2, pp. 305-317, 2007. https://doi.org/10.1016/j.ffa.2005.09.004
  14. T. Helleseth and P. Rosendahl, "New pairs of m-sequences with 4-level cross-correlation," Finite Fields and Their Applications, Vol. 11, No. 4, pp. 674-683, 2005. https://doi.org/10.1016/j.ffa.2004.09.001
  15. Y. Niho, "Multi-valued Cross-Correlation Functions Between Two Maximal Linear Recursive Sequences", Ph.D. thesis, University of Southern California, 1972.
  16. S.W. Golomb and G. Gong, Signal Design for Good Correlation, Cambridge University Press, 2005.