The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지

A New M-ary Sequence Family Constructed From Sidel'nikov Sequences

Sidel'nikov 수열로부터 생성한 새로운 M-진 수열군

  • 김영식 (삼성전자) ;
  • 정정수 (삼성전자) ;
  • 노종선 (서울대학교 전기.컴퓨터공학부 및 뉴미디어통신공동연구소) ;
  • 정하봉 (서울대학교 전기.컴퓨터공학부 및 뉴미디어통신공동연구소)
  • Published : 2007.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

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.

이 논문에서는 $M|p^n-1$를 만족하는 양의 정수 M과 소수 p에 대해서 주기가 $p^n-1$인 M-진 Sidel'nikov 수열을 사용해서 M-진 수열 군을 생성하였다. 이 수열군은 상관 값의 최대간이 $3\sqrt{p^{n}}+6$을 상한으로 갖고 수열군의 크기는 p=2일 때 $(M-1)^2(2^{n-1}-1)$+M-1 이거나 p가 홀수인 소수일 때는 $(M-1)^2(p^n-3)/2+M(M-1)/2$가 된다.

Keywords

References

  1. V. M. Sidel'nikov, 'Some k-valued pseudo-random sequences and nearly equidistant codes,' Probl. Inf. Transm., vol. 5, no. 1, pp. 12-16, 1969
  2. Y.-S. Kim, J.-S. Chung, J.-S. No, and H. Chung, 'On the autocorrelation distributions of Sidel'nikov sequences,' IEEE Trans. Inf. Theory, vol. 51, no. 9, pp. 3303-3307, Sep. 2005 https://doi.org/10.1109/TIT.2005.853310
  3. R. Lidl and H. Niederreiter, Finite Fields, vol. 20 of Encyclopedia of Mathematics and Its Applications. Reading, MA: Addison-Wesley, 1983
  4. D. Wan, 'Generators and irreducible polynomials over finite fields,' Mathematics of Computations, vol. 66, no. 219, pp. 1195-1212, July 1997 https://doi.org/10.1090/S0025-5718-97-00835-1
  5. 김영식, 정정수, 노종선, 정하봉, 'New constructions of the family of -ary sequences with low correlation,' 한국통신학회 추계종합학술대회 논문집, vol. 34, 2006년 11월, p.56
  6. P. V. Kumar, T. Helleseth, A. R. Calderbank, and A. R. Hammons, Jr., 'Large families of quaternary sequences with low correlation,' IEEE Trans. Inf. Theory, vol. 42, no. 2, pp. 579-592, Mar. 1996 https://doi.org/10.1109/18.485726
  7. P. V. Kumar, T. Helleseth, and A. R. Calderbank, 'An upper bound for Weil exponential sums over Galois rings and applications,' IEEE Trans. Inf. Theory, vol. 41, no. 2, pp. 456-468, Mar. 1995 https://doi.org/10.1109/18.370147
  8. S.-C. Liu and J. F. Komo, 'Nonbinary Kasami sequences over GF(p),' IEEE Trans. Inf. Theory, vol. 38, pp. 1409-1412, July 1992 https://doi.org/10.1109/18.144728
  9. R. Gold, 'Maximal recursive sequences with 3-valued recursive crosscorrelation functions,' IEEE Trans. Inf. Theory, vol. 14, pp. 154-156, Jan. 1968 https://doi.org/10.1109/TIT.1968.1054106
  10. H. M. Trachtenberg, 'On the cross-correlation functions of maximal recurring sequences,' Ph.D. dissertation, Univ. of Southern California, Los Angeles, CA, 1970