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

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Linear Complexity and 1-Error Linear Complexity over $F_p$ of M-ary Sidel'nikov Sequences

M진 Sidel'nikov 수열의 $F_p$ 상에서의 선형복잡도와 1-오류 선형복잡도

  • 정진호 (포항공과대학교 전자전기공학과 통신 및 신호설계 연구실) ;
  • 양경철 (포항공과대학교 전자전기공학과 통신 및 신호설계 연구실)
  • Published : 2006.12.30
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Abstract

In this paper we derive some lower bounds on the linear complexity and upper bounds on the 1-error linear complexity over $F_p$ of M-ary Sidel'nikov sequences of period $p^m-1$ when $M\geq3$ and $p\equiv{\pm}1$ mod M. In particular, we exactly compute the 1-error linear complexity of ternary Sidel'nikov sequences when $p^m-1$ and $m\geq4$. Based on these bounds we present the asymptotic behavior of the normalized linear complexity and the normalized 1-error linear complexity with respect to the period.

본 논문에서는 $M\geq3$이고 $p\equiv{\pm}1$ mod M인 경우에 대해서 주기가 $p^m-1$인 M진 Sidel'nikov 수열의 $F_p$ 상에서의 선형복잡도의 하계와 1-오류 선형복잡도의 상계를 유도한다. 특히 $m\geq4$이고 $p\equiv-1$ mod 3인 경우에는 3진 Sidel'nikov 수열의 정확한 1-오류 선형복잡도를 계산한다. 이 결과들을 바탕으로 선형복잡도와 1-오류 선형복잡도의 주기에 대한 비율의 근사적 특성을 제시한다.

Keywords

References

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