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

Korea Institute of Electronic Communication Science (한국전자통신학회)
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Four-Valued Cross-Correlation Function between Two Maximal Linear Recursive Sequences

최대 주기의 두 선형 순환 수열 사이의 4개의 값을 갖는 상호상관함수

  • 최언숙 (동명대학교 자율전공학부) ;
  • 조성진 (부경대학교 응용수학과) ;
  • 김한두 (인제대학교 컴퓨터응용과학부)
  • Received : 2012.08.06
  • Accepted : 2012.12.10
  • Published : 2012.12.31
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Abstract

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.

수열이론의 중요한 문제 중 하나는 두 수열사이의 상호 상관관계가 몇 개의 서로 다른 값을 가지며 또한 그 값의 발생횟수이다. 본 논문에서는 주기가 $2^n-1$인 m-수열 u(t)와 그 수열을 d만큼 데시메이션해서 얻은 수열 $u(dt)(0{\leq}t{\leq}2^n-2)$사이의 상호상관관계의 값과 그 값의 발생 횟수를 찾는다. 여기서 n=2m, 2s|m 이고, $d=(2^{2m}+2^{2s+1}-2^{m+s+1}-1)/(2^s-1)$ 이다. 또한 제안된 데시메이션에 의해 생성된 수열이 4-값 상호상관관계를 가짐을 보인다.

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References

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